' +JJJJ ?\>m0M='+l> /+l   d]@ŵLҦ]]L L}BBL] 鷎귭෍ᷩ췩緈JJJJx Lȿ L8ᷭ緍췩 緍i 8 `巬 췌`x (`(8`I`B` ``>J>J>VU)?`8'x0|&HhHh VY)'&Y)xꪽ)' `Hh`V0^*^*>&` aI꽌ɪVɭ&Y&&Y& 꽌ɪ\8`&&꽌ɪɖ'*&%&,E'зЮ꽌ɪФ`+*xS&x'8*3Ixix&& 8  '  & x)*++`FG8`0($ p,&"_]` L/浍굺L  !"#$%&'()*+,-./0123456789:;<=>?  1#"""  (9"1 ( ,.(0# 2  /#0/#0 *?'#07#00/0/'#07#0:"4<*55/**5/*%5/)1/)1/)1/)'#0/#0*5/*75/**5/*:5//#0/#0'#07#0:::*::'#07#0EB H  @H !D)"E` @ $ C ` DQ &J80^݌Hh ü ü݌ ռ ռ ռA ļD ļ? ļAEDE?HJ>h Լ ռ ռ ռ`HJ>݌h Hh݌`HIHHHHhHH݌hHhHh݌H6 ˆʎõĵL õ ĵµ aµ`` L̦µ_bJLuLz`  ȟ QlXJ̥KlV  ȟ QlV eօ3L e3L &RL &QL d L4 Ne)n `@-eff L f`L . tQLѤ LҦL` OPu d L Ne)noon 8ɍ` ^f\õL ^NR  RΩLҦ)\Z ʽ LHv 3h`0h8` [L NС õ`A@` ŵL^L iõ`  \ 濭0 \  ȟ Q ^\lZl^?cqH şch`fhjõĵ@OAP`u@`@&`QR`E Ls  @DAE@u`8` %@ @A@`@`@A`Mµ ) LЦ`8@AWc@8@-@HAȑ@hHȑ@ȑ@hHȑ@Ȋ@ch8&ȑ@Hȑ@Ah@LHȑ@ȑ@ htphso`hMhL`9V8U897T6S67`NONFORLOASAVRUCHAIDELETLOCUNLOCCLOSREAEXEWRITPOSITIOOPEAPPENRENAMCAMONOMOPRINMAXFILEFINBSAVBLOABRUVERIF!pppp p p p p`" t""#x"p0p@p@@@p@!y q q p@  LANGUAGE NOT AVAILABLRANGE ERROWRITE PROTECTEEND OF DATFILE NOT FOUNVOLUME MISMATCI/O ERRODISK FULFILE LOCKESYNTAX ERRONO BUFFERS AVAILABLFILE TYPE MISMATCPROGRAM TOO LARGNOT DIRECT COMMANč$3>L[dmx ( խŠ@跻~!Wo*9~~~~ɬƬ~_ j ʪHɪH`Lc (L ܫ㵮赎 ɱ^_ J QL_Ls贩紎 DǴҵԵƴѵӵµȴ 7 ַ :ŵƴѵǴҵȴµ納贍﵎ٵ്ᵭⳍڵL^ѵ-I `  4 ò-յ!  8صٵ紭ﵝ 7L (0+BC  7L HH`LgL{0 HH` õL H hBL BH [ h`Lo õ ڬL B ڬ LʬH hB@ յյ [L (ȴ) ȴ 7L L ( L (ȴL{ƴѵ洩ƴǴҵ 7 ^* B0 HȱBh ӵԵ 8 L8 ݲ` ܫ  / / ED B / / ]ƴS0Jȴ ȴ)  紅D贅E B ƴ  / 0L Ν `HD٤DEEhiHLGh ` ŵBѵ-` ѵB-` ܫ XI볩쳢8 DH E𳈈췍Ȍ X0 · JLǵBȵC`,յp` 䯩 R-յյ`յ0` K R-յյ`ɵʵӵԵ` 4 K ( ѵҵLBȱBL8` DBHBH : ַ޵BȭߵBhhӵԵ RBܵmڵ޵ȱBݵm۵ߵ` 䯩LR˵̵ֵ׵`êĪLR E( 8` R` ELRŪƪ`췌 յյI뷭鷭귭ⵍ㵍跬ª 뷰` Lf ݵܵߵ޵ ^`8ܵ i B8` 4L ֵȱB׵ ܯ䵍൭嵍 ` DȑB׵Bֵ  ַ յյ`굎뵎쵬 뵎쵌``õĵBCõĵ`µµ`L õBĵCصص Qƴ0"Bƴ 󮜳` 0۰ϬBƴ8`i#`ЗLw!0>ﵭ` m ﳐ 7i볍 8 ЉLw`H h ݲL~ `浍국䵍뵩嵠Jm赍嵊mjnnn浈m浍浭m䵍䵐`"L ŵ8ŵH ~(` d ֠Ġz# uSSS-`   vLDcpq` [` ~  LJfȹJ.J&J&fȹJ.J&Jf*))3)f)JJJ`V0^*^*` 2JfJȽ3J&J&f3ȽfJ&J&ffHA>VDP (ED Z $0x8x D- ܸDD# H8`?E Vk *f???0xE Hh D#-EEE8` D ܸx D - ܸx8`-0ݩ?ʥD EEE`Xj 0x D$xxH` ( Zh ZL.xxH hh@(LH9LHH/Hh/ H-З( ܸ(& ¸$8 H` *H݌h Hh݌`, HH`9`HIHHHHhHH݌hHhHh݌H6 h Լ ձ !"#$%&'()*+,-./0123456789:;<=>?? 03,+-(((((((((((((((((((((((((  03,+14434((((((((((((((((((((( 0335(((((((((((((((((((((((((('8*3Ixix&& 8  '  & x)*++`FG8`0($ p,&"_]` L/ `Hh`V0^*^*>&` aI꽌ɪVɭ&Y&&Y&ސ 꽌ɪ\8`&&꽌ɪɖ'*&%&,E'зސ꽌ɪ`+*xS&xGx (`(8`I`B` ` `>J>J>VU)?`8'x0|&HhHh VY)'&Y)xꪽ)'      (4)"LOCK"T$:0:1002:(0:1002:2LINE #":2:"IN PROGRAM"+ ':2:"CAUSE:"G 'I2023:I:7:26):I "'21:9:"EDUWARE SERVICES, INC.":8:"SAN FRANCISCO, CA 94107"::  NT$"AM3.ERR":(4)"UNLOCK"T$:(4)"OPEN"T$:(4)"WRITE"T$:(251):(253)(254)256:(252):(4)"CLOSE":CTRL C]":SG$"REBOOT DISK"L 9:10:ER$::14:(253)(254)256:14:PR$t :36,8:CS$::36,19(SG$)2:SG$ 4I110000:I:20000 >2110 ':I14:I:13:14):I '2:15:"ALGEBRA 3":14:"ERROR REPORT" '9:2:"ERROR:"::2:"AT ER$"DISK FULL":CS$"ADDITIONAL FILES SAVED ON DISK":SG$"DELETE THE ADDITIONAL FILES":2000 T1%14T1%77ER$"OUT OF MEMORY":CS$"YOU MAY NOT HAVE 48K OF MEMORY":SG$"TRY REBOOTING DISK":2000 8T1%255ER$"[CTRL C] INTERRUPT":CS$"YOU TYPED [NSERT DISK PROPERLY":2000 (T1%4T1%8)T1%13T1%254ER$"DOS ERROR #"(T1%):CS$"WRONG DISK MAY BE IN DRIVE":SG$"INSERT ALGEBRA VOLUME 3 DISK":2000 T1%8ER$"MEDIA ERROR":CS$"DISK MAY BE DAMAGED":SG$"TRY REBOOTING DISK":2000] T1%9DU-WARE,ALGEBRA 3,AM3.1,AM3.1.1,AM3.2,AM3.3,AM3.3.1,AM3.4,AM3.4.1,AM3.5,AM3.5.1 T1%4(T1%14T1%70)(T1%89T1%225)ER$"PROGRAM ERROR #"(T1%):2000 T1%4ER$"DISK IS WRITE-PROTECTED":CS$"DISK HAS A WRITE-PROTECT TAB":SG$"REMOVE TAB AND I 63900`AM3.ERROR COPYRIGHT (C) 1982, 1984 EDUWARE SERVICES, INC. ALL RIGHTS RESERVEDqVERSION 1.5{ 10000:1002:::10000:T1%(252):T2%(251)O ER$"UNKNOWN ERROR":CS$"UNDETERMINABLE":SG$"CONSULT EDU-WARE":I0T2%:PR$::E     *N(4)"CLOSE":35339:L*N26:(4)"UNLOCK"F$:(4)"OPEN"F$:(4)"WRITE"F$*NI15:C(I)::(4)"CLOSE":(4)"LOCK"F$:35339:*(222)255Ħ*25:::"++ ERROR ++"::" ERROR "(222)" AT LINE "(218)(219)256": AM3.5.1":P3:4400:920:R4:5400Z)r922:36309,1:36301,NR(3):36302,NR(4):26:(4)"RUNALGEBRA 3"h)'X9:L262)'X,YHX,YXL,YXL,YHX1,YHX1,Y:XL1,YXL1,YH:) N26:(4)"OPEN"F$:(4)"READ"F$:I15:C(I)::C(1)5:W3C(1)1:C(2)3C(2)6*"S$" into the spaces@D2H@provided.@I@":Y92:H64:9999:LBGEN:504:378("@2H12V@THE SOLUTION SET OF@2H16V@IS@4H14V@";:602:"@L3H17V@"(123)" , "(125)R$:510:N(5)(N(8)):N(7)(N(10)):O$(4)"-":O$(5)O$(4):800(z321::C4388({)pR2H16V@<4> Solve@21H@"V$(1)"=-"N(8)" or "V$(1)"=-"N(10):380y'"@2H17V@<5> Find@D6H@solution set@3F@(-"N(8)",-"N(10)")"'321::388I(A5:386:"@2H5V@Solve the "Q$" below@D2H@by putting it into standard form and@D2H@"F$"ing it. Then enter its@D2H@F@"N(1)V$(1)"@UG@2@RD@+"N(2)V$(1)"+"N(3)"=0@D6H@form":380:"@2H11V@<2> Factor@9F@("N(4)V$(1)"+"N(5)")("N(6)V$(1)"+"N(7)")=0":380;'"@2H12V@<3> Let each@7F@("N(4)V$(1)"+"N(5)")=0@D6H@factor@24H@or@D6H@equal@21H@("N(6)V$(1)"+"N(7)")=0@D6H@zero":380:"@."D$"<3> Set each "F$" containing the@D6H@variable equal to zero."D$;|%f"<4> Solve each of the resulting@D6H@"E$"s.":930%402:H24:9999:X12:135X,60135X,68::W$"SOLVE":L14:406:378:"@9H5V@";:602&"@2H8V@<1> Put into@D6H@standard@7the denominators."D$"<3> Combine like terms in the left@D6H@"M$"."D$;{$\"<4> Set the right "M$" equal to@D6H@zero.":930E%d600:W$"To solve a "Q$" by@D2H@"F$"ing:"D$"<1> Put the "E$" into standard@D6H@form."D$"<2> Factor the left "M$" of the@D6H@"E$"he"D$;J#"numbers for which at least one of"D$"its "M$"s is zero.":930`#PP5210,5220,1200E$Z600:W$"To put an "E$" into standard@D2H@form:"D$"<1> Remove all parentheses."D$"<2> Transform fractions into@D6H@integers by multiplying the@D6H@"E$" by @+@133C@5@10C@X@138C@+@133C@4@138C@=@133C@0"R$::930#W$"The standard form of a quadratic"D$E$" in one variable is@L3H9V133C@A@10C@X"R$"2@L138C@+@133C@B@10C@X@138C@+@133C@C@138C@=@133C@0@R15C10V@."D$"You can solve the "Q$D$"by "F$"ing it and finding tD$"linear "E$:940:"."X!"@14H15VL133C@3@10C@X@138C@+@133C@5@138C@=@133C@0"R$:930! W$"An "E$" of "P$" two is a"D$;:HD$Q$:940:".@2H13V@An "E$" of "P$" three is a"D$;:HD$"cubic "E$:940:"."5" X01:"@L133C5H"108X"V@3@10C@X"R$X2"@L138C17V10C@X"R$"2@L138C@-@133C@10@10C@X@138C@=-@133C@21"R$:321:"@L22H17V138C@+@133C@21@138C@=@133C@0"R$:930!W$"The ";:HD$"Degree of a Polynomial Equation":940:D$"in standard form is the "P$" of "D$"the polynomial. If it is of "P$D$"one, it is a ";:H,5130,5140,1200W$"A ";:HD$"Polynomial Equation":940:" is an"D$E$" whose left and right "M$"s"D$"are polynomials. It is in"D$;:HD$"Standard Form":940:" when one of its"D$M$"s is zero and the other is a"D$"polynomial";j " in simple form.@L11H)N$(2)"@15C@)("N$(3)V$"@138C@"O$(3)N$(4)"@15C@)@138C@=@133C@0"R$"@2H15V@HAS THE SOLUTION SET@L3H17V@"(123)" , "(125)R$:O$(2)"+"N(5)N(5)6510:O$(3)"+"N(7)N(7)8800321::C3388M5100,5200,5300,5400P5110,5120nto the spaces provided.@I@":Y76:H80:9999:LBGEN:410:378:362:5002I17:N(I)0::I132:374:II4:368:N(I3)N(I)N(I4):N$(I3)"@L133C@"(N(I3)):II4::N(5)N(7)O$(2)O$(3)44024"@2H10V@THE EQUATION@L2H12V@("N$(1)V$"@138C@"O$(2"@16V"138X"H@"V$(1)"="O$((A(X1)1))N(X):"@26H16V@or"D$;:380:"<4> Solution set@3F@(";:X12:"@"193X"H@"O$((A(X1)1))N(X)",";::"@B@)"321::388I0A3:386:"@2H5V@Solve the "E$" below. Then enter@D2H@both "M$"s of its "S$"@D2H@iN$(X)"@15C@)";::"@138C@=@133C@0"R$:382:"@2H10V@<1> State problem@2F@";:X12:"("V$(1)O$(X1)N(X)")";::"=0"D$;:380."<2> Write as@7F@("V$(1)O$(2)N(1)")=0@D6H@compound@9F@or@D6H@sentence@7F@("V$(1)O$(3)N(2)")=0"D$;:380:"<3> Solve":806:X12:ERO-PRODUCT AXIOM OF REAL NUMBERS"D$" For all real "N$"s A and B,"D$" AB=0 if and only if A=0 or B=0.":930402:H32:9999:W$"Find the "S$" for":L14:404:378:362:500I12:368::N(1)N(2)4301z"@L2H6V@";:X12:"("V$"@138C@"O$(X1)form.@8H14V@";:400:930"W$"Suppose we had the "E$"@2H7V@";:400:"@26H8V@."D$"For this to be true, either X-2=0 or "D$"X-1=0. So, X would have to be equal"D$"to 2 or 1. The "S$" is"D$"therefore (2,1).":930hP4210,1200krY36:H56:9999:W$" Z@D4B@PRODUCT"v"@L133C15H4U@0@138C@*@10C@X@138C@=@133C@0"R$:200,140168,140168,136166,138:168,136170,138:930W$"These properties of zero can help"D$"you find solutions of "E$"s in"D$"which one "M$" is zero and the"D$"other "M$" is in "F$"ed 4000,5000,6000)M4100,4200,4300,4400DP4110,4120,4130,1200 W$"As you know, the product of zero"D$"and any other real "N$" is zero."D$"Also, if the product of any two real"D$N$"s is zero, then at least one"D$"of the two "N$"s is zero.@4D@ZEROION@2D4H@<2> RULE@2D4H@<3> EXAMPLE@2D4H@<4> SAMPLE PROBLEM@2D4H@<0> RETURN TO CONTENTS@6D5HI@WHICH ONE (0-4) ??@I@"MN%0:MX%4:300:CH%İ922:26:(4)"RUNAM3."(36310)P1:MCH%:920:36320M,(36320M)(36320M)255P1200900:C2@":R$"@R0K15C@":W$R$"@2H5V@":N$"number":E$"equation":F$"factor":M$"member":S$"solution set":P$"degree":Q$"quadratic equation":O$(0)"-":O$(1)"+"LC(36312):P0:M0:900tC5ī1225sP0:M0:900:"@12H5V@MODE SELECTION@2D4H@<1> DISCUSS310:KY1289316250:KY136İ922:PP1:1220SKY149İ920:PP1:1220\931(36)2):X(36)73:Y(37)82:HD$" ";:L(HD$)76:H11:1000035339:R(I)((1)I):BG(36313):EN(36314):A(3),O$(5),N$(10),N(10)D$"@2D2H(X)"",:."@1H1V@C"C" P"P"@D1H@M"M:Z"@I2V7H@"31):24(HD$)2:HD$"@I@":j31051:924u30976"@21V1HI@"38)"@D1H@"38)"@I@":"@5H21VI@PRESS "(1)" TO VIEW THE NEXT PAGE.@3H22V@PRESS "(2)" TO VIEW THE PREVIOUS PAGE.@I@"@138C@=-"N$(3)R$:W R$"@26H16V@";:T(0)N(5)T(1)N(7)ĭT(0)N(7)T(1)N(5)804t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z"@L15C@(@10C@X@138C@-@133C@2@15C@)(@10C@X@138C@-@133C@1@15C@)@138C@=@133C@0"R$:Y36:H120:9999:X12:135X,68135X,156::"@L2H6V@"12):408"@L8H5V@"15)R$:BY8(C3):BX2:BH10(C4):BW2:N$(I)"@L133C@"(N(I)):[366:"@IR@":BX2:BY5:BHA:BW36:360:Y36:H(A1)8:9999j922:1200"@IL"V"V"H"H@ "KY(16384):KY128392250:KY171KY173ĺ"@200X40YN@":392"@IL"V"V"H"H@"(KY)R$;:KY171TA(0)TA(0)1:Z1133C@"(N(I)):F tAA$"":AB$"":IA$"":X01:AA$(X)"":TA(X)0::q vN(I)R(8)2:N$(I)"@L133C@"(N(I)): xN(I)N(I)1(R(2)): zPL:900 |AI075:310:: ~AI037:310:: N(I)R(5)1:N$(I)"@L133C@"(N(I)):N(I)R(4)$"":I0PS%:IN$IN$((256I)):I:IN(IN$):"@R@":IA$IA$IN$:p hBIBYBYBH1:"@"BX"H"BI"V@"BW):BI: jX12:VR(6)84:V$(X)(V)::V$(1)V$(2)362 lV$(3)V$(1)V$(2):V$"@L10C@"V$(1): n3:14,39265,39: pN(I)R(9)1:N$(I)"@L352@ a250:HT%PS%F:((256PS%));:KY155ESC%1:"@R@":T bKY141PS%359n cKY136PS%PS%PS%1 dKY149PS%MX%PS%PS%1 eKYKY128:(KY47)(KY58)(KY45PS%0)ĖHT%PS%F:(KY);:256PS%,KY:PS%PS%1:PS%MX%359 f351C gIN"@22V1HI@..PRESS (SPACE BAR) TO CONTINUE...":250H C310:KY128323^ E250:KY160323x H"@22V1H@"36)"@I@": ^VB%:HT%:MX%):PS%0:I0MX%:256I,32:I:16368,0:F2ĺ"@L@" _HT%PS%F:"@I@"((256PS%))"@I@"; `310:KY128KY149CH%MN%CH%MX%300 2C 6GG(1):KY(16384):290:KY155ıZ 8250:"@40X40YN@";| :KY(16384):290:KY128314 ;250:KY155Ĺ36309,0:26:(4)"RUNALGEBRA 3" <KY205Mı =319 >:318 ?63900 @"@R15C0K@":922:12003 A"24576:30719:63900(AM3.5.1lCOPYRIGHT 1982 EDU-WARE SERVICES, INC. ALL RIGHTS RESERVED F$"AM3.PROGRESS":10000:1002P::16368,0:"XXR(1):,310:KY128300.250:KY155CH%0 0CH%KY176:          ,9:252,(222):253,(218):254,(219):(4)"RUNAM3.ERROR":1UNAM3.ERROR":11OR":11218)(219)256": AM3.5"1:B$(I)::2'X9:L262[2'X,YHX,YXL,YXL,YHX1,YHX1,Y:XL1,YXL1,YH:2PÃFactoring Quadratic Trinomials,Combining Factoring,Zero Products,Solving Polynomial Equations,Quadratic Trinomial Test,1,2,3,5,72(222)255Ħ<380:251NM(3,K,R)NM(1,J,I)1(O3$"-")1tB$(NI)B$(NI)"@20H@"(A)" + "(B)" = "(AB):ABN(2)B$(NI)B$(NI)"@35H138C"((7))"V@<--@15C@"1uNINI1:R,K,J,I:I18:JI18:(B$(I),5,14)(B$(J),5,14)(B$(I),19,14)(B$(J),5,14)J9:J,I: 2xAM3.5.1":<0BG1:EN4:R1:2400:920:R2:3400:920:40000pI19:B$(I)""::NI1:I01:J1P(1):K1P(3):R01:B$(NI)"@2H@("(NM(1,J,I))SV$O3$(NM(3,K,R))")("(NM(1,J,I))SV$O4$(NM(3,K,R))")"#1rANM(1,J,I)NM(3,K,R)1(O4$"-"):Bents of the "F$"s into the@D2H@spaces provided.@I@":Y84:H72:9999:LBGEN:Y11:H8:400:378/J 362:"@2H11V@FACTOR":Y11:H10:GR(2):Gİ500:512:806:3498/\ 510:512:CA(2)CA(3):CA(3)N(3):806/ 321::C2388/ 0200:80:(4)"RUNFind greatest common factor@2H11VL@("N$(3)V$"@15C@)("N$(4)V$R$"2@L138C@-"N$(5)"@15C@)"R$"@2H14V@2) Factor the difference of two@D6H@squares":Y17:H2:516:930_/H A4:392:"@2H5V@Factor the "P$" below@D2H@completely. Then enter the numerical@D2H@coefficiP23307- W$"FACTOR":402:900:Y5:H10:500:"@2H9V@1) Find greatest common factor@2H11VL@("N$(4)V$"@15C@)("N$(5)V$R$"2@L138C@+"N$(6)V$"@138C@+"N$(7)"@15C@)@R2H14V@2) Factor the trinomial"- Y16:H2:504:930. 402:900:Y5:H10:510:"@2H9V@1) ce of two squares@D6H@and "F$" it.", "@2H13V@3) If it is a "T$", find all@D6H@"B$" "F$"s.@D2H@4) Repeat all steps until there are@D6H@no more "F$"s. Then write the@D6H@answer as a "S$" of all@D6H@"F$"s.":930- P51200:Y36:H120:9999:H24:9999:me and"D$"monomial "F$"s are left.":9309+ P3210,1200#, Y36:H120:9999:W$"To "F$" a "P$" completely:"D$"1) Factor out any monomial "F$"s@D6H@from the "P$". Then@D6H@consider the remaining "F$".@D2H@2) If it is a "B$", see if it@D6H@is the differens with"D$"integral coefficients. Such"D$P$"s are called ";:HD$"prime":940:" over"D$"this set.":930(+0 W$"To ";:HD$"Factor a Polynomial Completely":940:D$"means to find the prime "F$"s of a"D$P$". The "F$"ing process"D$"must continue until only priTA(0,1)TA(1,2)TA(0,2)TA(1,1):CA(3)TA(0,2)TA(1,2):800N) 321::C1388T) o) M3100,3200,3300,3400) P3110,3120,1200f*& W$"Some "P$"s, such as@L2H7V10C@X"R$"2@L138C@+@10C@X@138C@+@133C@1"R$"@8V@, can not be "F$"ed"D$"over the set of "P$"38C@"O1$"@133C@"(N(2))"@10C@"V$"@138C@"O2$"@133C@"(N(3))"@2H15V138C@=@5H15C@( "V$" @15C@)( "V$" @15C@)"R$(h X01:VB%16:HT%816X:F2:MX%1:350:TA(X,1)IN:MX%2:FL9:HT%1416X:350:TA(X,2)IN::700:CG2408:)j CA(1)TA(0,1)TA(1,1):CA(2)78:362'c I0:372:GR(4)1'd I47:N(I)PN(R(5)1)::N(R(4)4)1:N(8)N(4)N(7):N(9)N(5)N(6):G410,420,430,440:N(2)2404'e K29:N(1)K(N(1)K)N(2)K(N(2)K)N(3)K(N(3)K)K10::2403q(f :"@L133C4H12V@"N(1)"@10C@"V$"@R15C@2@L1";:454&_ 930&` A5:392:"@2H5V@Find both "P$" "F$"s of the@D2H@"T$" given below. Test all@D2H@possible pairs of "F$"s until you@D2H@find the correct result. Then type@D2H@it into the spaces provided.@I@":Y92:H64:9999'b LBGEN:Y12:H7:400:33))R$"@2H13V@are@D3H@";:SV$"":I3:460:321:400j% SV$R$V$(1):R$"@2H8V@Try@20H@Linear term@D@":6000% 321:Y8:H11:400:360:"@2H9V@One possible set of "B$" "F$"s@D2H@that produces a linear term similar@D2H@to that of the "T$" is:"& "@9H17V@ms of@2D2H@the "B$" "F$"s is @L133C@"N(1)V$R$"2"D$"and the "S$" of the constant@2D2H@term is @L133C@"(N(3))R$:321:4001% R$"@2H8V@The possible "F$"s of @L133C@"N(1)V$R$"2@D2H@are@D3H@";:SV$R$V$(1):I1:460:"@2H12V@The possible "F$"s of @L133C@"(N(H@"T$".":930#P51200`#Y36:H24:9999:H120:9999:R$"@2H5V@FACTOR":Y8:H11:400:362#I47:N(I)PN(R(5)1)::N(R(4)4)1:N(8)N(4)N(7):N(9)N(5)N(6):P410,420,430,440:N(2)2302x$ 450:321:400:R$"@2H9V@The "S$" of the linear ter@D6H@the last term of the "T$".":321:Y11:H8:400:"@2H11V@3) When the first term of each" #"@6H12V@"B$" is multiplied by the@D6H@second term of the other@D6H@"B$", and the results are@D6H@added, the sum must be equal to@D6H@the middle term of the@D6ust find two "B$"s with@D2H@these traits:@L4H6V@"A1$"+"A2$"+"A3$"@7V@,@2H11V@1) The "S$" of the first terms@D6H@of both "B$"s must be equal"\""@6H13V@to the first term of the@D6H@"T$"."D$"2) The "S$" of the last terms of@D6H@both "B$"s must be equal to8C@+@133C@E@R15C12H13V@and@L16H12V133C@F@10C@X@138C@+@133C@G"; J"@R15C13V@. You must"D$"list and try all possible pairs of"D$F$"s until you find a solution.":930 P2210,1200!Y36:H48:9999:H120:9999:W$"To "F$" a quadratic "T$",@3D2H@you m1H@"A2$"@I@"w@321:"@11H9V@"A2$"@I17H@"A3$"@I@":321:"@17H9V@"A3$"@21H12V@and a degree of"D$"two.@I8H9V@2@I@":930> HW$"Factoring a "P$" of the form@2H7V@"A1$"+"A2$"+"A3$"@8V@ is the reverse of"D$"multiplying "B$"s of the form@2H12VL133C@D@10C@X@13P1200-900:C2000,3000,4000,4000,5000HM2100,2200,2300,2400^4P2110,2120,1200 >W$"A ";:HD$"Quadratic Trinomial":940:" is written"D$"in the form@4H9V@"A1$"+"A2$"+"A3$"@10V@."D$"It has three terms@I4H9V@"A1$"@I@":321:"@4H9V@"A1$"@I1"@12H5V@LEARNING MODES@2D4H@[1] Discussion@2D4H@[2] Rule@2D4H@[3] Example@2D4H@[4] Sample Problem@2D4H@[0] Return to Concept Menu@6D5HI@Which ([0]-[4]) ??@I@"MN%0:MX%4:300:CH%İ922:1100P1:MCH%:920:36320M,(36320M)(36320M)255@D14H@Equations@D10H@[5] "CH$(5)d`"@10H15V@[0] Return to Unit Menu@6DI11H@Which ([0]-[5]) ??@I@"eMN%0:MX%5:300:CCH%:Cİ922:80:(4)"RUNALGEBRA 3":jHD$CH$(C):910:920nC3C44000tC5P0:M0:1225P0:M0:BG1:EN9:900:,13243,138:31,11431,12628,123:32,11432,12635,123:"@3H16V@[0]"dZ59,3259,15960,15960,32 ["@20H5V@CONCEPTS":X23:"@14H"7X"V@"CH$(X)::X24:"@10H"7X"V@["X"]"::"@10H7V@[1] Factoring Quadratic@D14H@Trinomials@3D14H@Solving Polynomial:P0:M0:900:HD$"":910:X18:Y3810216:H12:L27:10000:(Y10)8:"@3H@["(Y22)16"]"VY102ēX13,Y12X13,Y16:X10,Y13X13,Y16:X14,Y12X14,Y16X17,Y13EX:21,13814,13221,12642,12649,13242,13820,13813,13220,126:43,12650)A$:C$(1,3)"a sum and a difference.":C$(2,1)A$:C$(2,2)A$:C$(2,3)"sums.":C$(3,1)N$:C$(3,2)N$:C$(3,3)C$(1,3):C$(4,1)A$:C$(4,2)N$:C$(4,3)"differences."(36309)2BG1:EN4:R5:2400:36303,NR(5):920:80:(4)"RUNALGEBRA 3":[L36309,0:C05:PN(I):W$"@R15C2H5V@":D$"@2D2H@":R$"@R15C0K@":P$"polynomial":B$"binomial":F$"factor":T$"trinomial":S$"product":A$"positive":N$"negative":A1$"@L133C@A@10C@X@R15C@2@L138C@":A2$"@L133C@B@10C@X@138C@":A3$"@L133C@C"R$C$(1,1)N$:C$(1,2he Last Page@I@"/10:KY8İ922:PP1:1220KKY21İ920:PP1:1220T932(36)2):X(36)73:Y(37)82:HD$1):L(HD$)76:H11:10000 35339:R(I)((1)I):I15:CH$(I)::F2:FG0:C$(4,3),NM(3,2,4),N(11),N$(11),TA(2,2):I1ER IS":321:Y17:H2:G1504,516A"@1H1V@C"C" P"P"@D1H@M"M:m"@I2V7H@"31):24(HD$)2:HD$"@I@":}31051:92430976"@21V1HI@"38)"@D1H@"38)"@I@":"@3H21VI@Press ["(1)"] to View the Next Page@3H22V@Press ["(2)"] to View t(KY78KY110)700 [ R$"@3H18V@";:N(1)CA(1)N(2)CA(2)N(3)CA(3)804x""RIGHT":NR(R)NR(R)1:$"ANSWER IS@U3H@WRONG,@13H@";:454:&R$"@3H18V@";:(N(1))(CA(1))(N(2))(CA(2))(N(3))(CA(3))802!("@U@WRONG, ANSWTA(0,2)TA(1,1)):CA(3)TA(2,1)TA(0,2)TA(1,2):"@"Y"V"H"HL15C@("N$(3)V$"@15C@)("N$(6)V$"@138C@+"N$(7)"@15C@)("N$(6)V$"@138C@-"N$(7)"@15C@)"R$:CG0:"@I21V2H@Do You Want to Change Your Answer?@D16H@[Y or N]@I@"10:924:KY89KY121CG1: "V$"@15C@)@D6H@( "V$" @15C@)( "V$" @15C@)"R$F2:MX%1:VB%14:HT%5:350:TA(2,1)IN:VB%16:X01:MX%1:HT%916X:350:TA(X,1)IN:MX%2:HT%1516X:350:TA(X,2)IN::700:CG5141CA(1)TA(2,1)TA(0,1)TA(1,1):CA(2)TA(2,1)(TA(0,1)TA(1,2)$"@15C@)("N$(8)V$"@138C@+"N$(9)"@15C@)("N$(10)V$"@138C@+"N$(11)"@15C@)"R$:362:I3:374:I67:374::N(4)N(6)N(6):N(5)N(7)N(7):N(1)N(3)N(4):N(2)N(3)N(5):N(1)N(2)510:A1:B7:376:"@"Y"V"H"H@"N$(1)V$R$"3@L138C@-"N$(2)V$R$:4"@L2H13V@(11:374::N(5)N(8)N(10):N(6)N(8)N(11)N(9)N(10):N(7)N(9)N(11):N(1)N(4)N(5):N(2)N(4)N(6):N(3)N(4)N(7):A1:B11:376N(8)N(9)N(10)N(11)500"@"Y"V"H"H@"N$(1)V$R$"3@L138C@+"N$(2)V$R$"2@L138C@+"N$(3)V$R$:K"@"Y"V"H"HL15C@("N$(4)V(@133C@"N(4)V$"@138C@"O3$"@133C@"N(5)"@15C@)(@133C@"N(6)V$"@138C@"O4$"@133C@"N(7)"@15C@)"R$:T0:X1(N(I))2:X(N(I))X(N(I))X((N(I))X)ĺX;SV$"*"(N(I))X;SV$1):TT1:NM(I,T,0)X:NM(I,T,1)(N(I))X:P(I)T:362:I4:374:I8"@L133C10H5V@"N(1)"@10C@"V$"@R15C@2@L138C@"O1$"@133C@"(N(2))"@10C@"V$"@138C@"O2$"@133C@"(N(3))R$"@2H9V@The constant term, "N(3)", is "C$(P,1)".""@2H@The linear term, "N(2)", is "C$(P,2)".@D2H@So, the two "B$" "F$"s are@D2H@"C$(P,3):]"@L@1$:408NO1$"+":O2$O1$:O3$O1$:O4$O1$:N(2)N(8)N(9):N(3)N(5)N(7):404O1$"-":O2$O1$:N(3)(N(5)N(7)):N(7)N(4)N(5)N(6)O3$"+":O4$O1$:406O4$"+":O3$O1$:408O1$"-":O2$"+":O3$O1$:O4$O1$:N(2)N(8)N(9):N(3)N(5)N(7):404A:BW36:360:Y36:HA88:9999B R$:BX2:BYY:BHH:BW36:360c "@L8H5V@"15):Y9:H10:400x N(1)N(4)N(6): N(2)N(9)N(8):404 N(2)N(8)N(9):404 O1$"+":O2$"-":N(3)(N(5)N(7)):N(9)N(8)O3$O1$:O4$O2$:406O3$O2$:O4$O:V$(X)("AEMNRTXY",R(8)1,1)::V$(1)V$(2)362[ lV$(3)V$(1)V$(2):V$"@L10C@"V$(1):n tN(I)R(4)1: vN(I)PN(R(4)1): xIAB:N$(I)"@L133C@"((N(I))):: zPL:900 3:14,39265,39: 920:1200 384:"@IR@":BX2:BY5:BH(IN$):"@R@":IA$IA$IN$:IAIAIN:FL0:K aFL9PS%KY43KY45352l c(KY8KY127)PS%PS%PS%1 eKY47KY58PS%MX%PS%(KY45KY43)ĖHT%PS%F:(KY);:256PS%,KY:PS%PS%1 f352 hBIBYBYBH1:"@"BX"H"BI"V@"BW)::1 jX12; AR$"@21V3HI@Press [SPACE BAR] to Continue@I@":16368,0O E10:KY32325Z H924:j ^F2ĺ"@L@" _VB%:HT%:MX%):PS%0:I0MX%:256I,0::16368,0* `HT%PS%F:"@I@ @BI@";:10:" @B@";:KY13PS%IN$"":I0PS%:IN$IN$((256I))::IN%KY48:CH%MN%CH%MX%300" 2I 6GG(1):KY(16384)128:KY27ıe 816368,0:"@40X40YN@"; :KY(16384)128:KY0314 ;16368,0:KY27Ĺ36309,0:80:(4)"RUNALGEBRA 3" <KY77Mı =319 >:318 ?63900 @R$:922:1200>+ 63900\AM3.5 COPYRIGHT (C) 1982, 1984 EDUWARE SERVICES, INC. ALL RIGHTS RESERVEDt 24576:30719:1000 310:KY010 16368,0:P0:1002::36312,C:X12:(36298X),NR(X)::36313,BG:36314,EN:,10:KY27KY48 0CH                )(219)256": AM3.4.1":P:C(I)::C(1)5:W3C(1)1:C(2)3C(2)6D,*N(4)"CLOSE":35339:y,N26:(4)"UNLOCK"F$:(4)"OPEN"F$:(4)"WRITE"F$,NI15:C(I)::(4)"CLOSE":(4)"LOCK"F$:35339:,(222)255Ħ-25:::"++ ERROR ++"::" ERROR "(222)" AT LINE "(2184400:920:R4:5400X+r922:36309,1:36301,NR(3):36302,NR(4):26:(4)"RUNALGEBRA 3"s+P6110,6120,6130,1200+XR3:6400:5002+'X9:L262+'X,YHX,YXL,YXL,YHX1,YHX1,Y:XL1,YXL1,YH:*, N26:(4)"OPEN"F$:(4)"READ"F$:I15ign as@D2H@";*"the linear coefficient, "N(3)",@D2H@but only "N(1)"-"N(2)" = "N(3)".@L138C22H10V@+@133C@"N(1)"@138C32H@-@133C@"N(2)R$*321::922:1200*500:LBGEN:406:372:370:Z$"-":462:504:806*n321::C4İ922:1200*o+pR3:nce the constant term is "S$",@D2H@we must then find two "N$"s such@D2H@that one is "S$; *" and another is@D2H@"A$".":321:406:"@2H13V@-";:A1$"-":A2$"":480:"@2H14V@-";:A1$"":A2$"-":480:"@2H15V@The one with the largest@D2H@"AV$" has the same sH@"A$". The one with the@D6H@greatest "AV$" has the@D6H@same sign as c.@D2H@<3> If the trinomial is reducible,@D6H@its "F$"s are X+a and X+b."(\930X)460:L14:402:Z$"-":462:"@2H8V@"L$"@L138C@ =@18H10V15C@("V$" @15C@)("V$" @15C@)"R$"@2H12V@Si$" must be "S$".":930' W$"However, if both AB and A+B are"D$S$", then the one with the"D$"larger "AV$" is "S$","D$"while the other is "A$".":930'PP5210,1200(ZZ$S$:450:"@2H12V@<2> One of the two "N$"s a and b@D6H@is "S$" and the other is@D6$"@2H10V@If you were to put it in the form@2H12V@"C$"@2H15V@you would notice that A+B is "A$D$"and AB is "S$".":930'W$"For AB to be "S$" and A+B to be"D$A$", then the one of A or B with"D$"the larger "AV$" must be"D$A$". The one with the smaller"D$AVS$;%".":321::922:1200U%0500:LBGEN:406:372:370:Z$"+":462:504:800p%321::C3İ922:1200v%%M5100,5200,5300,5400%P5110,5120,5130,1200t&W$"Look at the "P$" below:@L2H7V10C@X"E$"@L138C@+@133C@2@10C@X@138C@-@133C@8"R82:"@2H11V@"V$E$"@L6H138C@=@9H@"V$"@138C@*"V$"@10H8V@"V$"@20H@"V$R$:380:"@2H14V@";:A1$"":A2$"":480$"@7H15V@But only "N(1)"+"N(2)"="N(3)"@12H8V@"O$N(1)"@22H@"O$N(2)R$:380:"@2H17V@"O$R$" because the linear term is@D5H@";:N(0)0ĺA$;:4308%h a@D6H@and b must be "A$". If c is@D6H@"S$", then a and b must be@D6H@"S$".@D2H@<3> If there are no such "N$"s a@D6H@and b then it is irreducible,@D6H@else its "F$"s are X+a and X+b":930#460:L14:402:Z$"+":462h$380:"@L8H8V@( )( )"R$:3into "P$"s of lesser degree."D$"Such "P$"s are called"D$;:HD$"irreducible":940:". If their greatest"D$"monomial "F$" is one, they are"D$"called ";:HD$"prime "P$"s":940:".":930"hP4210,1200"rZ$A$:450#t"@2H12V@<2> If c is "A$", then botC@.@R2H8V@The constant term, 6, can be the"D$"product of two "A$" or two"D$S$" "N$"s. But the linear"D$"term, -5X, can not be the sum of two"D$A$;!B"s. Only two "N$"s will"D$"work. The "F$"s are (X-2)(X-3).":930"JW$"Some "P$"s cannot be "F$"ed"D$"term, ab,"D$"can be the product of two "A$D$"or "S$" "N$"s. But since"D$"the linear term, (a+b)X, is "A$","D$"only using two "A$" "N$"s for"D$"a and b will work.":930!@W$"Suppose we had@D2H@to "F$"@L18H5V10C@X"E$"@L138C@-@133C@5@10C@X@138C@+@133C@6@15@+@133C@A@15C@)(@10C@X@138C@+@133C@B@15C@)@D10H138C@=@13H@"C$:380:"@L2H15V@(@10C@X@138C@+@133C@2@15C@)(@10C@X@138C@+@133C@3@15C@)"."@10H17V138C@=@13H10C@X"E$"@L138C@+@133C@5@10C@X@138C@+@133C@6"R$:930 6"@4H5V@"C$"@2H8V@Notice that the constant and "X"+ "93X" = "92X"@7HD@-"X"*-"93X" and -"X"+-"93X" = -"92X$:380:"@30H13V@"(2):213,107238,107:"@2H16V@So, 2 and 3 are the only "N$"s"D$"that will work.":930,W$"Now let's substitute 2 and 3 for"D$"A and B.@L2H9V@(@10C@X@138Cthat,@L3H16V133C@A@138C@+@133C@B@138C@=@133C@5"R$"@15H17V@and@L16V20H133C@AB@138C@=@133C@6@15C@."R$:930K"W$"So, we need to find two "N$"s that"D$"equal 5 when added, and equal 6 when"D$"multiplied.":380:"@3H11V@6 =":X12:"@8H"92X"V@"X"* "93X"10C@X"E$"@L138C@+@133C@5@10C@X@138C@+@133C@6"R$:380:"@1H8V@If it were@D1H@written as:@16H8V@"C$:380:"@1H11V@Its "F$"s@D1H@would be:@L16H11V10C@X@138C@+@133C@A"R$h"@23H12V@and@L27H11V10C@X@138C@+@133C@B"R$:380:"@1H14V@In that case, we would know A@138C@+@133C@B@15C@)@10C@X";:380:"@138C@+@133C@AB"R$:380:X185:Y173:X288:Y2103:400:"@14H9V@These two "B$"s are@D14H@the "F$"s of:":380X1190:Y1113:X2193:Y2127:400:"@29H14V@This@D29H@"P$:930W$"@B@Suppose we had@D1H@to "F$":@L16H5V,4300,44009P4110,4120,4130,4140,4150,4160,4170,1200W$"Watch as these two "B$"s are"D$"multiplied.@L3H9V10C@X@138C@+@133C@A@1H11V138C@*@10C@X@138C@+@133C@B":5:X12:8,107X63,107X::3:380:"@L3H14V10C@X"E$;:380"@L138C@+@15C@(@133C@PLE@2D4H@<4> SAMPLE PROBLEM@2D4H@<0> RETURN TO CONTENTS@6D5HI@WHICH ONE (0-4) ??@I@"MN%0:MX%4:300:CH%İ922:26:(4)"RUNAM3."(36310)P1:MCH%:920:36320M,(36320M)(36320M)255P1200900:C24000,5000,6000 M4100,4200@10C@X@138C@+@133C@AB"R$2AV$"absolute value"|(36309)2BG1:EN4:R4:5400:36302,NR(4):920:26:(4)"RUNAM3.5"LC(36312):P0:M0:900tC5ī1225TP0:M0:900:"@12H5V@MODE SELECTION@2D4H@<1> DISCUSSION@2D4H@<2> RULE@2D4H@<3> EXAM1:10000<35339:R(I)((1)I):BG(36313):EN(36314)D$"@2D2H@":R$"@R0K15C@":W$R$"@2H5V@":E$R$"2":S$"negative":N$"number":F$"factor":P$"polynomial":B$"binomial":A$"positive":C$"@L10C@X"E$"@L138C@+@15C@(@133C@A@138C@+@133C@B@15C@)"@5H21VI@PRESS "(1)" TO VIEW THE NEXT PAGE.@3H22V@PRESS "(2)" TO VIEW THE PREVIOUS PAGE.@I@"w310:KY128931250:KY136İ922:PP1:1220KY149İ920:PP1:1220931(36)2):X(36)73:Y(37)82:HD$" ";:L(HD$)76:H1)Q(1)N(2)802q("ANSWER IS@U7H@WRONG,@L17H@("V$"@138C@+@133C@"N(1)"@15C@)("V$"@138C@-@133C@"N(2)"@15C@)"R$:"@1H1V@C"C" P"P"@D1H@M"M:"@I2V7H@"31):24(HD$)2:HD$"@I@":31051:92430976"@21V1HI@"38)"@D1H@"38)"@I@":bY,1)" "T3$T3$(AB$,IY,1)=:IA$T1$:AA$T2$:AB$T3$:~ 700:R$"@7H18V@";:TA(N(0)0)2804:IA$AA$IA$AB$804""RIGHT":NR(R)NR(R)1:$"ANSWER IS@U7H@WRONG,@L17H@";:X12:"@L@("V$O$N(X)"@15C@)"R$;::&R$"@7H18V@";:Q(0)N(10:MX%2:F2:VB%15:HT%1212X:350:Q(Z)(IN$):_AA$(N(1))(N(2)):AB$(N(2))(N(1)):T1$"":T2$"":T3$"":IY1(IA$):(IA$,IY,1)" "T1$T1$(IA$,IY,1):IY1(AA$):(AA$,IY,1)" "T2$T2$(AA$,IY,1):IY1(AB$):(AB$,Iinomial given below is@D2H@reducible over the set of "B$"s@D2H@with coefficients that are integers.@D2H@Find both of the "P$"'s@D2H@"F$"s.@I@"Y92:H64:9999:1"@L138C2H15V@=@5H15C@";:X12:"@L@(@10C@"V$" @15C@)"R$;::X01:V15:H912X:390O$"@L138C@-@133C@"6404:N(4)25N(1)N(2)462NM3ĺ"@10H5V@"L$:a"@4H12V@"L$:N(4)"= ";:X1N(4)2:XN(4)XĭN(4)X(N(4)X)ĺA1$X"*"A2$N(4)X" ";:Y36:H48:9999:"@I@":BX2:BY5:BH5:BW36:360:366:"@2H5V@The tr= a+b and d = ab.":BY36:H24:9999:H120:9999:W$"FACTOR":370:362:O$"@L138C@+@133C@":I02:368::I0:376:C3R3ĭN(I)0O$"@L138C@-@133C@"C3R3N(3)N(1)N(2):404:N(4)36N(4)48N(4)72462C4R4N(3)N(1)N(2):N(3)"@133C@"(N(4))R$:4BX2:BY12:BH7:BW36:360Y36:H40:9999:H120:9999:W$"To "F$" trinomials of the form@3D3H@such that d is a "Z$" "N$":@L6H6V10C@X"E$"@L138C@+@133C@C@10C@X@138C@+@133C@D"R$"@2H10V@<1> Find two "N$"s a and b such@D6H@that c V"H"H@"(KY)R$;:KY171TA(0)TA(0)1:Z0GKY173TA(1)TA(1)1:Z1MX12:X2X,Y1X2X,Y2::X1,Y1X2,Y1:X1,Y2X2,Y2:"@L10H5V@"9)R$:BX2:BY8:BH11:BW36:360V$"@L10C@"V$:N(4)N(1)N(2):L$V$E$O$((N(3)))V$"@138C@"Z$:IA$"":X01:AA$(X)"":TA(X)0::7 vN(I)R(8)2:R xN(I)N(I)1(R(2)):h |AI075:310::~ ~AI037:310:: AI025:310:: "@IL"V"V"H"H@ " KY(16384):KY128392 250:KY171KY173ĺ"@200X40YN@":392)"@IL"V"IN$IN$((256I)):I:IN(IN$):"@R@":IA$IA$IN$:b hBIBYBYBH1:"@"BX"H"BI"V@"BW):BI: jX12:VR(6)84:V$(X)(V)::V$(1)V$(2)362 lV$(3)V$(1)V$(2):V$V$(1): n3:14,39265,39: pN(I)R(9)1: rPL:900$ tAA$"":AB$""352@ a250:HT%PS%F:((256PS%));:KY155ESC%1:"@R@":T bKY141PS%359n cKY136PS%PS%PS%1 dKY149PS%MX%PS%PS%1 eKYKY128:(KY47)(KY58)ĖHT%PS%F:(KY);:256PS%,KY:PS%PS%1:PS%MX%359 f3515 gIN$"":I0PS%:"@22V1HI@..PRESS (SPACE BAR) TO CONTINUE...":250H C310:KY128323^ E250:KY160323x H"@22V1H@"36)"@I@": ^VB%:HT%:MX%):PS%0:I0MX%:256I,32:I:16368,0:F2ĺ"@L@" _HT%PS%F:"@I@"((256PS%))"@I@"; `310:KY128KY149CH%MN%CH%MX%300 2C 6GG(1):KY(16384):290:KY155ıZ 8250:"@40X40YN@";| :KY(16384):290:KY128314 ;250:KY155Ĺ36309,0:26:(4)"RUNALGEBRA 3" <KY205Mı =319 >:318 ?63900 @"@R15C0K@":922:12003 A%24576:30719:63900(AM3.4.1lCOPYRIGHT 1982 EDU-WARE SERVICES, INC. ALL RIGHTS RESERVED F$"AM3.PROGRESS":10000:1002P::16368,0:"XXR(1):,310:KY128300.250:KY155CH%0 0CH%KY176:                           AT LINE "(218)(219)256": AM3.4": 218)(219)256": AM3.4":1f)"WRITE"F$A0NI15:C(I)::(4)"CLOSE":(4)"LOCK"F$:35339:0PÃ"TRINOMIAL SQUARES","MULTIPLYING BINOMIALS","SUMS OR DIFFERENCES","SUMS AND DIFFERENCES","FACTORING AND BINOMIALS TEST"0(222)255Ħ&125:::"++ ERROR ++ "::" ERROR "(222)"920:R2:3400:920:4000&/'X9:L262f/'X,YHX,YXL,YXL,YHX1,YHX1,Y:XL1,YXL1,YH:/ N26:(4)"OPEN"F$:(4)"READ"F$:I15:C(I)::C(1)5:W3C(1)1:C(2)3C(2)6/*N(4)"CLOSE":35339: 0N26:(4)"UNLOCK"F$:(4)"OPEN"F$:(4+@10C@"N(4)"@15C@)@138C4H14V@=@10C13H@"V$R$"2@L138C@+ @10C@"V$"@138C@+"R$:MX%3:VB%15:HT%8:350.L HT%19:350:HT%29:350:412:AA$(N(5))(N(8))(N(9)):810. 321:L:C2İ922:1200. .200:26:(4)"RUNAM3.4.1"/BG1:EN4:R1:2400:ltiply the two "B$"s below@D2H@together. Then enter the numeric@D2H@coefficients of the "P$" in the@D2H@spaces provided.@I@":Y84:H72:9999:LBGEN:406:378:386c.J 362:I14:368::"@L4H11V@(@10C@"N(1)V$"@138C@+@10C@"N(2)"@15C@)(@10C@"N(3)V$"@138C@8C@+@10C@"N(2)N(3)V$"@138C28H@=@10C31H@"N(8)V$R$:382:"@2H15V@<3>@L10H10C@"N(2)"@138C@*@10C@"N(4)"@28H138C@=@10C31H@"N(9)R$:382, "@2H17V@ANSWER@L10H10C@"N(5)V$R$"2@L138C@+@10C@"N(8)V$"@138C@+@10C@"N(9)R$,G 321::922:1200-H A4:392:"@2H5V@Mu:"@2H9V@<1>@L8H@(@10C@"N(1)V$"@15C@)(@10C@"N(3)V$"@15C@)@138C@ =@10C31H@"N(5)V$R$"2":382:"@2H11V@<2>@L8H@(@10C@"N(1)"@138C@*@10C@"N(4)"@15C@)@10C@"V$"@138C@+@15C@(@10C@"N(2)"@138C@*@10C@"N(3)"@15C@)@10C@"V$, "@10H13V138C@=@R@ @L10C@"N(1)N(4)V$"@13erms of the@D6H@"B$"s together.@D2H@<4> Add all of the "P$"s.":930* Y36:H32:9999:H120:9999:W$"MULTIPLY":L14:410:378:362:I14:368::"@L8H6V@(@10C@"N(1)V$"@138C@+@10C@"N(2)"@15C@)(@10C@"N(3)V$"@138C@+@10C@"N(4)"@15C@)"R$* 412+ 38296:9999:W$"To find the "P$" of two "B$"s@D2H@of the form aX+b and cX+d."D$"<1> Multiply the first terms of the@D6H@"B$"s together.@D2H@<2> Multiply the first term of each@D6H@"B$" by the last term of the@D6H@other "B$;C* ".@D2H@<3> Multiply the last t of degree one."(, "@15H11V@It is called a@D15H@Linear Term.@I@"A2$"@I@":321:408:A2$R$"@15H9V@The last term is@D15H@numeric with no@D15H@variable factor. It is@D15H@called a Constant Term.@I@"A3$"@I@":321:A3$R$( 930( P3210,1200) Y36:H14V@BD":A1$"@L138C10H14V@+"A2$"@L138C28H14V@+"A3$R$:321:Y68:H40:L168:X100:10000(* R$"@15H9V@Look at the first term.@D15H@It is of degree two in@D15H@X. It is called a@D15H@Quadratic Term.@I@"A1$"@I@":321:408:A1$"@R15H9V@The second term@D15H@isultiply these two "B$"s"D$"together.@L3H9V133C@A@10C@X@138C@+@133C@B@1H11V138C@*@133C@C@10C@X@138C@+@133C@D"R$:5:X12:8,107X76,107X::3:321V'( A1$"@L133C3H14V@AC@10C@X@R15C@2":A2$"@L15C12H14V@(@133C@AD@138C@+@133C@BC@15C@)@10C@X":A3$"@L133C30H$"@2H14V@IS THE SQUARE OF THE BINOMIAL@D9H10CL@"V$R$:VB%16:HT%6:MX%2:350:FLAG9:MX%1:HT%12:350:FLAG0%h MX%2:HT%14:350:AA$(N(4))SG$((N(5))):800% 321:L:C1İ922:1200% % M3100,3200,3300,3400% P3110,1200&& W$"Let's mssing places of its root "B$".@I@":Y84:H72:9999:LBGEN:406:378$b 386:362:I45:368::I5:370:N(2)2(N(4)N(5)):"@2H11V@THE TRINOMIAL@D2HL10C@"(N(4)2)V$R$"2@L138C@";:SG$"+":N(5)0SG$"-"l%f SG$"@L10C@"(N(2))V$"@138C@+@10C@"(N(5)2)Rl to the@D6H@middle term,the@D6H@trinomial is:"#" "@L22H17V@(@10C@"N(4)V$(1)"@138C@"O$(P2)"@10C@"N(5)V$(2)"@15C@)@R@2":930E$` A4:392:"@2H5V@The "T$" below is either the@D2H@sum or difference of two terms.@D2H@Factor the "T$" and fill in the@D2H@mi<2> Find the last @D6H@term's square@D6H@root."v" "@L10C24H12V@"(N(5)2)V$(2)R$"2@L138C31H@=@R@ @L10C@"N(5)V$(2)R$/# 382:"@2H14V@<3> Find twice@D6H@their product.@L22H14V10C@2@138C@*@10C@"N(4)"@138C@*@10C@"N(5)V$(1)V$(2)R$:382:"@2H16V@<4> If equaL138C@"O$(P2)"@10C@"2(N(4)N(5))V$(1)V$(2)"@138C@+@10C@"(N(5)2)V$(2)R$"2":382:"@2H8V@<1> Find the first@D6H@term's square@D6H@root.":X155:Y84:404/" "@L10C24H9V@"(N(4)2)V$(1)R$"2@L138C31H@=@R@ @L10C@"N(4)V$(1)R$:382:X155:Y108:404:"@2H11V@@133C@"O$(P); "@10C@"V$(2)V$(1)"@138C@+@10C@"V$(2)V$(2)"@6H16V138C@= @10C@"V$(1)R$"2 @L133C@"O$(P)"@10C@2"V$(1)V$(2)"@138C@+@10C@"V$(2)R$"2":930  Y36:H24:9999:H120:9999:I45:368:146I,60146I,156::362! W$"@L10C@"(N(4)2)V$(1)R$"2@"difference@D2H@of two terms:" "@2H8VL@(@10C@"V$(1)"@133C@"O$(P)"@10C@"V$(2)"@15C@)@R@2 @L138C@= @15C@(@10C@"V$(1)"@133C@"O$(P)"@10C@"V$(2)"@15C@)(@10C@"V$(1)"@133C@"O$(P)"@10C@"V$(2)"@15C@)@6H12V138C@= @10C@"V$(1)V$(1)"@133C@"O$(P)"@10C@"V$(1)V$(2)"@D6H@the first and last terms."D$;"<4> If the middle term is negative,@D6H@the "T$" is a "S$" of a@D6H@difference instead of a sum.":930P2310,2310,2330,2330,1200 362:W$"This is how to "S$" the ";:P1ĺ"sum of two@D2H@terms:" P2ĺ= @10C@A@R15C@2@L133C@"O$(X)"@10C@2AB@138C@+@10C@B@R15C@2"::930"Y36:H120:9999:W$"If a "T$" is a "S$" of a@D2H@"B$":"D$"<1> The first term is a "S$"."D$"<2> The last term is a "S$"."D$"<3> The middle term is twice the@D6H@"P$" of the "S$" roots of@138C@+@10C@B@R15C@2 @L138C@= @15C@(@10C@A@133C@"O$(X)"@10C@B@15C@)@R@2"::930fP2210,2220,1200AY36:H88:9999:"@11H5V@Squaring a Binomial"D$"For all "B$"s with terms A and B":X12:"@L3H"54X"V@(@10C@A@133C@"O$(X)"@10C@B@15C@)@R@2 @L138C@22H@second term.@I@"A3$"@I@":321:A3$R$:930RW$"Whenever you "S$" a "B$", the"D$P$" will be a ";:HD$"Trinomial Square":940:"."D$"So, "T$"s of certain patterns"D$"are the "S$"s of "B$"s."PTX12:"@L10C3H"103X"V@A@R15C@2@L133C@"O$(X)"@10C@2AB@D22H@the "B$"'s@D22H@first term.@I@"A1$"@I@":321:400:A1$"@R22H11V@The second term@D22H@is twice the@D22H@"P$;-D" of the@D22H@"B$"'s first@D22H@and second term.@I@"A2$"@I@":321:400:A2$"@R22H11V@The third term@D22H@is the "S$" of@D22H@the "B$"'s@D72X"V@A@138C@"O$(P)"@10C@B":5:7,105X63,105X::3@A1$"@L15C3H14V@A@R@2@L@":A2$"@L15C6H14V@"O$(P)"2AB":A3$"@L15C14H14V@+B@R@2@L@":A1$A2$A3$:382qBY68:H64:L126:X142:10000:"@R21H9V@NOTICE THAT:@2D22H@The first term@D22H@is the "S$" of5P1:MCH%:920:36320M,(36320M)(36320M)255BP1200g900:C2000,3000,4000,4000,5000mM2100,2200,2300,24004P2110,2110,2130,12007>W$"Suppose we were to "S$" the"D$B$" A"O$(P)"B:":382:"@L1H11V138C@*":X12:"@10C3H"920nC3C44000,tC5P0:M0:1225P0:M0:900:"@12H5V@MODE SELECTION@2D4H@<1> DISCUSSION@2D4H@<2> RULE@2D4H@<3> EXAMPLE@2D4H@<4> SAMPLE PROBLEM@2D4H@<0> RETURN TO CONTENTS@6D5HI@WHICH ONE (0-4) ??@I@"MN%0:MX%4:300:CH%İ922:1100INOMIAL@D14H@";d\"SUM AND A BINOMIAL@D14H@DIFFERENCE@D10H@<5> FACTORING AND BINOMIALS@D14H@TEST"`"@10H17V@<0> RETURN TO ALGEBRA MENU@4DI11H@WHICH ONE (0-5) ??@I@"eMN%0:MX%5:300:CCH%:Cİ26:30976:(4)"RUN ALGEBRA 3"jHD$CH$(C):910:31,11431,12628,123:32,11432,12635,123:"@3H16V@<0>"XZ59,3259,15960,15960,32["@20H5V@CONTENTS":X12:"@14H"6X"V@"CH$(X)::X13:"@10H"6X"V@<"X">"::"@14H9V@THE PRODUCT OF BINOMIAL@D14H@SUMS OR DIFFERENCES@D10H@<4> THE PRODUCT OF A B:HD$"":910:X18:Y3810216:H12:L27:10000:(Y10)8:"@3H@<"(Y22)16">"VY102ēX13,Y12X13,Y16:X10,Y13X13,Y16:X14,Y12X14,Y16X17,Y139XY:21,13814,13221,12642,12649,13242,13820,13813,13220,126:43,12650,13243,138:(37)82:HD$" ";:L(HD$)76:H11:10000s36309,0:35339:R(I)((1)I):BG1:EN9:I15:CH$(I)::F2:FG0W$"@R15C2H5V@":D$"@2D2H@":R$"@R15C0K@":O$(1)"+":O$(2)"-":S$"square":B$"binomial":P$"product":T$"trinomial"NLC0:P0:M0:900"@21V1HI@"38)"@D1H@"38)"@I@":"@5H21VI@PRESS "(1)" TO VIEW THE NEXT PAGE.@3H22V@PRESS "(2)" TO VIEW THE PREVIOUS PAGE.@I@"310:KY128931250:KY136İ922:PP1:1220KY149İ920:PP1:1220931*(36)2):X(36)73:Y8C@"SG$(N(5))R$:7*700:R$"@12H16V@";:IA$AA$802,"WRONG, ANSWER IS@L138C7H17V@"N(5)"@10C@"V$R$"2@L138C@+"N(8)"@10C@"V$"@138C@+"N(9)R$:"@1H1V@C"C" P"P"@D1H@M"M:"@I2V7H@"31):24(HD$)2:HD$"@I@":31051:92430976 $"":IY1(IA$):(IA$,IY,1)" "T1$T1$(IA$,IY,1)p:IY1(AA$):(AA$,IY,1)" "T2$T2$(AA$,IY,1):IA$T1$:AA$T2$: 700:R$"@6H18V@";:IA$AA$804""RIGHT":NR(R)NR(R)1:$"WRONG, ANSWER IS@L138C24H17V@"N(4)"@10C@"V$"@13BY11:BH8:BW36:3618R$:BX15:BY9:BH4:BW23:361h"@8H6VL@"12)R$:BX2:BY9:BH10:BW36:361N(5)N(1)N(3):N(8)N(1)N(4)N(2)N(3):N(9)N(2)N(4):IN$"+ "IN$"- "IA$IA$IN$:454IA$IA$(IN):IAIA(IN$)7T1$"":T20::IA0:K384:"@IR@":BX2:BY5:BHA:BW36:361:Y36:H(A1)8:9999kY36:H104(16(P5)):9999R$:BX22:BY11:BH5:BW16:361W$"@L@"12)R$:BX2:BY8:BH11:BW36:3615:X,YX3,Y4X6,Y4X12,Y14X61,Y14:3:R$:BX2:4:V$(X)(V)::V$(1)V$(2)362@ lV$(3)V$(1)V$(2):V$V$(1):S nN(I)R(9)1:f pN(I)R(8)2: rN(I)N(I)1(R(2)): zPL:900 |AI0150:310:: ~AI0100:310:: 3:14,39265,39: AA$"":IA$"":PM$"":NP$"":X14:PA(X)%PS%1r fKYKY128:(KY42)(KY58)(KY45KY43PS%)ĖHT%PS%F:(KY);:256PS%,KY:PS%PS%1:PS%MX%360{ g351 hIN$"":I0PS%:IN$IN$((256I)):I:IN(IN$):"@R@":450: iBIBYBYBH1:"@"BX"H"BI"V@"BW):BI: jX12:VR(6)8ĺ"@UL@"1 _HT%PS%F:"@I@"((256PS%))"@I@";M `310:KY128KY149352z aFLAG9(KY171KY173)İ330:250:352 b250:HT%PS%F:VB%:((256PS%));:KY155ESC%1:"@R@": cKY141PS%360 dKY136PS%PS%PS%1 eKY149PS%MX%PS:318 ?63900. @"@R15C0K@":922:1200g AR$"@22V1HI@..PRESS (SPACE BAR) TO CONTINUE...":250| C310:KY128323 E250:KY160323 H"@22V1H@"36)"@I@": J"@200X40YN@": ^VB%:HT%:MX%):PS%0:I0MX%:256I,32:I:16368,0:F2 ,310:KY128300+ .250:KY155CH%0O 0CH%KY176:CH%MN%CH%MX%300U 2~ 6GG(1):KY(16384):290:KY155ı 8250:"@40X40YN@"; :KY(16384):290:KY128314 ;250:KY155İ26:(4)"RUNALGEBRA 3" <KY205Mı =319 >')24576:30719:63900&AM3.4jCOPYRIGHT 1982 EDU-WARE SERVICES, INC. ALL RIGHTS RESERVED F$"AM3.PROGRESS":10000:1002P::36312,C:X12:(36298X),NR(X)::36313,BG:36314,EN:16368,0:"XXR(1):                       "LOCK"F$:35339:#(222)255Ħz25:::"++ ERROR ++"::" ERROR "(222)" AT LINE "(218)(219)256": AM3.3.1":P"HX,YXL,YXL,YHX1,YHX1,Y:XL1,YXL1,YH: N26:(4)"OPEN"F$:(4)"READ"F$:I15:C(I)::C(1)5:W3C(1)1:C(2)3C(2)6*N(4)"CLOSE":35339:N26:(4)"UNLOCK"F$:(4)"OPEN"F$:(4)"WRITE"F$NI15:C(I)::(4)"CLOSE":(4)R$6X01:F2:MX%2:VB%14:HT%616X:350:Q(X,1)IN:V14:H1116X:390:MX%2:HT%1416X:350:Q(X,2)IN::AAN(1)N(2):8008321:L:C3İ922:1200R3:4400922:36309,1:36301,NR(3):26:(4)"RUNALGEBRA 3"'X9:L2626'X,Yts@D2H@first "F$" and then enter its@D2H@second "F$".@I@":Y84:H72:9999:LBGEN:408:3702372:362:I12:368:N(I)1N(I)24:"@L3H11V10C@"(N(1)2)V$R$"2@L138C@-@10C@"(N(2)2)"@138C17H@=@3H14V15C@( @10C@"V$" @15C@)( @10C@"V$" @15C@)"@L138C@-@10C@"N(1)R$"2@L2H16V@SO:(@10C@"V$"@138C@+@10C@"N(1)"@15C@)(@10C@"V$"@138C@-@10C@"N(1)"@15C@)@138C@=@10C@"V$R$"2@L138C@-@10C@"N(1)R$"2"321:L:922:1200\0R$:A4:406:"@2H5V@The binomial below is the "DF$"ce@D2H@of two "S$" "M$"s. Enter i362:I1:368:"@L2H4V@(@10C@"V$"@138C@+@10C@"N(1)"@15C@)(@10C@"V$"@138C@-@10C@"N(1)"@15C@)@3H7V138C@=@10C@"V$R$"2@L138C@+@10C@"N(1)V$"@138C@-@10C@"N(1)V$"@138C@-@10C@"(N(1)2)"@3H10V138C@=@10C@"V$R$"2@L138C@-@10C@"(N(1)2)"@3H13V138C@=@10C@"V$R$"210C@X"R$"2@L138C@-@10C@Y"R$"2 @L138C@= ";:402:R$:930|400:W$"The two "F$"s of a binomial which@D2H@is the "DF$"ce of two "S$"s@D2H@are:"D$"<1> The sum of the two "S$" roots."D$"<2> The "DF$"ce of the two "S$"@D6H@roots.":930L14:404:370:=@15C@(@10C@3@138C@+@10C@2@15C@)(@10C@3@138C@-@10C@2@15C@)"R$:930XhP4210,4220,12008r400:W$"To multiply the sum of two "N$"s@D2H@by the "DF$"ce of two "N$"s,@D2H@"S$" the first "N$" and subtract@D2H@from it the "S$" of the second@D2H@"N$".@L3H11V10C@X@R15C@2@L138C@-@10C@Y@R15C@2":930"W$"So, when you see a "P$" that is"D$"the "DF$"ce of two "S$D$M$"s, you'll know what its two"D$F$"s are.@L5H13V@(@10C@X@R15C@2@L138C@-@10C@Y@R15C@2@L@)@138C@=";:402B$"@5H16V@(@10C@9@138C@-@10C@4@15C@)@138C@45,64X:266X,64245,64X:266X,64245,64X:384:=930W$"The product of the sum of two "N$"s"D$"and the "DF$"ce of the same two"D$N$"s is equal to the "S$" of the"D$"first "N$" minus the "S$" of the"D$"second."'"@L6H15V@";:402:"@138C@=@"D$"in mathematics. If you learn"D$"to recognize them, they may"D$"help you to make shortcuts in"D$"solving some problems. One such"D$"pattern is a "P$" containing"D$"two "M$" "S$"s."4Y36:H56:X219:L51:10000:X0243:224X,64245,64X:224X,642?@I@"@MN%0:MX%4:300:CH%İ922:26:(4)"RUNAM3."(36310)vP1:MCH%:920:36320M,(36320M)(36320M)255P1200900:(36310)3ĴC24000,5000M4100,4200,4300,4400P4110,4120,4130,1200W$"Many "DF$"t patterns occurpolynomial":M$"monomial":O$(0)"+":O$(1)"-"ILC(36312):P0:M0:900XtC4ī1225P0:M0:900:"@12H5V@MODE SELECTION@2D4H@<1> DISCUSSION@2D4H@<2> RULE@2D4H@<3> EXAMPLE@2D4H@<4> SAMPLE PROBLEM@2D4H@<0> RETURN TO CONTENTS@6D5HI@WHICH ONE (0-4) ?:PP1:1220931^(36)2):X(36)73:Y(37)82:HD$" ";:L(HD$)76:H11:1000035339:R(I)((1)I):BG(36313):EN(36314):Q(2,2)-D$"@2D2H@":R$"@R0K15C@":W$"@R15C2H5V@":DF$"differen":S$"square":N$"number":F$"factor":P$"(HD$)2:HD$"@I@":#31051:924.30976T"@21V1HI@"38)"@D1H@"38)"@I@":"@5H21VI@PRESS "(1)" TO VIEW THE NEXT PAGE.@3H22V@PRESS "(2)" TO VIEW THE PREVIOUS PAGE.@I@"310:KY128931250:KY136İ922:PP1:1220 KY149İ920Y)N(Y)Q(1,Y)N(Y)8060":PS1SS1806M$"RIGHT":NR(R)NR(R)1:&"WRONG, FACTORS ARE":X01:382:"@L138C14V"516X"H@ @"516X"H@"N(1)"@"1116X"H@ @"1116X"H@"O$(X)N(2)R$::"@1H1V@C"C" P"P"@D1H@M"M:"@I2V7H@"31):241Y36:H72:9999_"@15C@(@10C@X@138C@+@10C@Y@15C@)(@10C@X@138C@-@10C@Y@15C@)";:R$:BX2:BY4:BH14:BW36:360366:"@IR@":BX2:BY5:BHA:BW36:360:Y36:H(A1)8:9999BX2:BY11:BH8:BW36:360 R$"@7H17V@";:Y12:Q(0,:PS0:SS0:TA0:X01:AA$(X)""::; |AI0150:310::R ~AI0100:310::h AI025:310::} "@IL"V"V"H"H@ " KY(16384):KY128392 250:KY171KY173ĺ"@200X40YN@":392 "@IL"V"V"H"H@"(KY)R$;:KY171PS1KY173SSIN$IN$((256I)):I:IN(IN$):"@R@":IA$IA$IN$:b hBIBYBYBH1:"@"BX"H"BI"V@"BW):BI: jX12:VR(6)84:V$(X)(V)::V$(1)V$(2)362 lV$(3)V$(1)V$(2):V$V$(1): n3:14,39265,39: pN(I)R(9)1: rPL:900$ tAA$"":IA$""352@ a250:HT%PS%F:((256PS%));:KY155ESC%1:"@R@":T bKY141PS%359n cKY136PS%PS%PS%1 dKY149PS%MX%PS%PS%1 eKYKY128:(KY47)(KY58)ĖHT%PS%F:(KY);:256PS%,KY:PS%PS%1:PS%MX%359 f3515 gIN$"":I0PS%:"@22V1HI@..PRESS (SPACE BAR) TO CONTINUE...":250H C310:KY128323^ E250:KY160323x H"@22V1H@"36)"@I@": ^VB%:HT%:MX%):PS%0:I0MX%:256I,32:I:16368,0:F2ĺ"@L@" _HT%PS%F:"@I@"((256PS%))"@I@"; `310:KY128KY149CH%MN%CH%MX%300 2C 6GG(1):KY(16384):290:KY155ıZ 8250:"@40X40YN@";| :KY(16384):290:KY128314 ;250:KY155Ĺ36309,0:26:(4)"RUNALGEBRA 3" <KY205Mı =319 >:318 ?63900 @"@R15C0K@":922:12003 A|24576:30719:63900(AM3.3.1lCOPYRIGHT 1982 EDU-WARE SERVICES, INC. ALL RIGHTS RESERVED F$"AM3.PROGRESS":10000:1002P::16368,0:"XXR(1):,310:KY128300.250:KY155CH%0 0CH%KY176:       ;"LOCK"F$:35339:>PÃ "PRIME FACTORS","MONOMIAL FACTORS","THE DIFFERENCE OF TWO SQUARES","SIMPLE FACTORING TEST",2,3,5,7,11,13,17,19,23,29,31,37>(222)255Ħ>25:::"++ ERROR ++ "::" ERROR "(222)" AT LINE "(218)(219)256": AM3.3":HX,YXL,YXL,YHX1,YHX1,Y:XL1,YXL1,YH:= N26:DX$;"OPEN"F$:DX$;"READ"F$:I15:C(I)::C(1)5:W3C(1)1:C(2)3C(2)6=*NDX$;"CLOSE":35339:=N26:DX$;"UNLOCK"F$:DX$;"OPEN"F$:DX$;"WRITE"F$>NI15:C(I)::DX$;"CLOSE":DX$@13H@( "V$(1)V$(2)")":F1:MX%2:VB%17:HT%15:IA0:350:TA$(1)IN$r<{ AA$(1)(N(1)):AA$(2)AA$(1):TA$(2)TA$(1)<| 812:321::C2İ922:1200< <200:26:(4)"RUNAM3.3.1"<BG1:EN4:R1:2420:920:R2:3400:920:4000<'X9:L2627='X,Y(2)PV$(2)") and@16H@( "PV$(3)"+ "PV$(4)")";L F1:MX%2:VB%17:HT%18:350:TA$(1)IN$:HT%22:350:TA$(2)IN$:AA$(1)(N(3)):AA$(2)(N(4)):3452C Find the greatest "M$" that@D6H@is a "F$" of each term of the@D6H@"P$"."D$"<2> Divide the "P$" by the@D6H@"M$" "F$;2 ". The quotient is@D6H@the other "F$"."D$"<3> Express the "P$" as the@D6H@product of the two "F$"s.":another"D$M$". Its numerical coefficient"D$"will be the square of the original"D$"one. It will also have the same"D$"variables, ";0< "but their powers will be"D$"doubled.":9300 P3210,3220,12001 Y36:H112:9999:W$"To "F$" a "P$" whose terms@D2F$"s in an "I$". The"D$;:HD$"Greatest Monomial Factor":940:" of a"D$P$" is the "M$" "F$D$"having the biggest numerical"D$"coefficient and degree.":9300: W$"When you square a "P$", you are"D$"using it as a "F$" twice. The"D$"square of a "M$" will be $"do this. For example,"D$"2XY+4X = 2X(Y+2). Both 2X and Y+2"D$"are "F$"s of 2XY+4X. 2X is called"D$;.( "a ";:HD$"Common Monomial Factor":940:" since it"D$"is a "M$".":930/0 W$"Finding the Common Monomial Factor"D$"of a "P$" is like finding "S$D$MX%3:HT%30:VB%14:F1:350:AAPA:806G- 321::C1İ922:BG1:1200M- h- M3100,3200,3310,3400- P3110,3120,3130,1200e.& W$;:HD$"Factoring a "P$:940:" means to"D$"write it as a product of "P$"s."D$"We can use the Distributive Axiom to"D COMMON@D22H@FACTOR?"6,v 406:LBGEN:402:378:PA1,x 410:N(1)10N(1)200N(3)10N(3)2002424:"@L133C3H13V@"(N(1))"@3H16V@"(N(3))R$,z X12:PR(1,X)PR(1,X2)2440,| PO(X)1:PR(2,X)PR(2,X2)PO(X)PR(2,X),~ PAPAPR(1,X)PO(X)'- :300:"@34H17V@"CH%"@I@":INCH%:806:321::920:BG5:EN9,t A4:392:"@2H5V@Factor the two large "N$"s in the@D2H@left box. Then find the largest@D2H@"N$" that is a "F$" of both, the@D2H@greatest common "F$".@I2H3D@FACTOR@22H@WHAT IS THEIR@D22H@GREATESTz#?    ͳҠͳӠ ͳ8 ͳͳ+ ͳ' ͳ-ͳ$ͳҠխŠӳ$ͳӠͳ3ͳ7ͳ5~6 6#33080<0 1 81$ 60~6#<0~< <?60<3>8<<0x? <899???16?830>>33?`?y$%GΩϩ  %%%GΩϩ  %%$$'к`&$%GΩϩ  %%%GΩϩ  %%$$м`  p 4114440 4004438 3883339 399398 9889997 977997 9779922 2222221 2112297 977998 98          (219):80:(4)"RUNAM3.ERROR":5185,97E "@R15C15H15V@2@20H@2@25H@2@L13H15V@a@16H@=b@21H@+c@R@":W (222)255Ħ :8:10:"ENCOUNTERING PROBLEMS":11:"WHILE BOOTING DISK"::7:"REINSERT DISK AND TRY AGAIN" 63902 X(222):X255Ħ 251,0:252,X:253,(218):254,188,56189,56179,67:"@R27H6V@"(22)"@IR15C@":VT1012:"@"VT"V23H@ "::"@I@" 6:A80:I161189.9:I,A189,A:AA1::3 140,80161,80:126,112188,112:140,81160,81:126,111188,111 3:167,83:173,87:179,82:185,84:175,91:183,90: 5:141,48196,72141,72141,48:142,49196,71142,71142,49 7:170,53168,55166,56165,58164,60163,64163,66164,68165,71166,73168,75170,77 171,53169,55167,56166,58165,60164,64164,66165,68166,71167,73169,75171,77T 178,67BRA VOLUME 3@R20V9H@Copyright "(21)" 1982, 1984@D9H@EduWare Services, Inc.@D10H@All Rights Reserved@I@"{ PRINT PICTURE 66,35213,35213,14766,14766,35:67,36214,36214,14867,14867,36 1:I7791:I,48I42,96::I7791:I,96I42,48:?35339:I3629936351:I,0:J150:J,I:80:(4)"RUNALGEBRA 3":T PRINT BOARDERS 5,6275,6275,1855,1855,64,6274,6274,1854,1854,6 LPRINT HEADERS WITH A BACKGROUND V"@RI@":I23:I:2:38)::I2123:I:2:38):h `"@L1V4H@ALGE"1012,0:63900eEDU-WARE COPYRIGHT (C) 1982,1984 EDUWARE SERVICES INC. ALL RIGHTS RESERVED24576:27903:205,255:3::::1:12:"ALGEBRA VOLUME 3":(4)"BLOADEWS3":63905 500P0:1002::@ :35339::35397,32:230,64:1000:      >>" r6<& " " ""  >"""6&""""""!"" 0  A<& * Ax"" >``@x0   p""W06 >>8>0>>><""""<>""!"">>> 8 ( >6 `>`@x>> 8 D "LU :F`F`$L"%e%`$e($`%80%`$80$`'$L:{|0L_`F)׭F F)L i)`) qp`<) Ji L? Ji L? d d Z P F < 2 (  2222P2(2F2 2<(LI GIG`RH`GH`LH`E yIy`OF) ELSSzI zU`TR`P EI E`NLUX F{LY F|LTIF eiLȱ|ȱ{ U`FFB DLF .L`% ImE8Ie$e΅ϩeeυ GIy) e$) =}м`0:)F FmFeF`@D`C r)׍} ~  `K r)׍ `H F($LV F%@ JTL J UEPWRz6F GFy 7 ?` !!""## ( !(!"("#(# P !P!"P"#P# ((ˍ) J ?`DLk@D` LH5Ω " .Ωz % $L.jjΩ .@0~~@@|@>f@@@@ 0 0@pp @@@@@@@p@0`x@@@0@@@pp|@|x0`@ @0| @0|| @L << @ 00 0pf>>fff@@@@@@ |@@@@@@@pp@0 x@pp|||p0pp@0@ |p|| p pp | p p |@p@ @|||@p@@@@@@p@ ||@@``@|@@@`x6r@|`0@ @0 0|| @L << @ 0 0x0pff@@@@@@ |@@@`@xp@@@?p6@0 ~@x@|p||||0|p0@| |||| | p| | | | |@|@ @|||@pp`@@@@@@|@ |@@`@x@@@`pF@00@@ @@ < @@ < @ < @ 0 0p0`|||||||@@@@@@@@@p@@~pp@X@?pF0 p`@@<@ 0 @@@| @ @ 0< @ x0p```````@@@@@@ 0<00@@@@p@@?``6r@00p`@@ p @ 0 @@ 0 @ @ 0xxxxxxx@@@@@@@@@x`x@@f|p||@p6000@@<@ 0 @@@@| @ @ 0<0@ 0xxxxxxx@@@@@@ 0<00@@@@`@?``@00x@x|p|||p~||0||p|||||| p |||||| || |00```````@@@@@@@0```|@`|||xpp@@|00@l@<| 0 @0|@| @L LL@ L0@0 0|||||||@@@@@@ L@p@@@@@@@`~x@00`p@|||@~pp0p|@|p|||p p p|p|p| || |@@0@@@@@@@0`x@@`~|x`ppp6x@|00`@l@0| 0 0|@|| @L L L@ L0@0 0f>@@@@@@ L@|@@@@`~@0@@@@@@@~~@@|`~ppppp|F@0@`||~L@@@ |@pp@ ||| || |@< LL | |p@ @@@ @ 0ff>>fff@@@@ 0 0`0???6$?30>>0<0~ <1<$33>>?3?oducts":Z$(5,4)"Polynomials"Z$(6,1)"Monomials":Z$(6,2)"Polynomials":Z$(6,3)"Factoring":Z$(6,4)"Binomials":Z$(6,5)"Trinomials"X17:Y44:L246:H112:10000:L203:H64:Y60:10000:X2137:X213717841:X2,60X2,124X21,124X21,60:n"@I,3)Z$(1,3):Z$(3,1)"Prime Factors":Z$(3,2)"Monomial Factors":Z$(3,3)"Diff. of Squares"Z$(4,1)"Trinomial Square":Z$(4,2)"Binomials":Z$(4,3)"Sums or Differ.":Z$(4,4)"Sums and Differ.":Z$(5,1)"Factoring":Z$(5,2)"Combine Factors":Z$(5,3)"Zero Pr(6)"POSTTEST"h 24(S$(CH%))2:"@1V@"S$(CH%)"@I@":36310,CH%:80:CH%6Ĺ36309,2:(4)"RUNAM3.1": (4)"RUNAM3."CH%: UN(36310):Z$(1,1)"Add and Subtract":Z$(1,2)"Multiplication":Z$(1,3)"Division"YZ$(2,1)Z$(1,1):Z$(2,2)Z$(1,2):Z$(2,2546,5:5,165274,165:5,25274,25} "@0VI@":G12:"@7H@"32)""::"@21V1H@"38)"@D1H@"38):49,7272,7:7,167272,167 S$(1)"MONOMIALS":S$(2)"POLYNOMIALS":S$(3)"SIMPLE FACTORING":S$(4)"FACTORING AND BINOMIALS":S$(5)"QUADRATIC TRINOMIALS":S$S$(4)"SAMPLE PROBLEM"z 15:6:"MODE USAGE":I14:I28:8:S$(I);:Z(T(I)100T):32((Z)):Z"%":::21::30000 CH%9C(1)6:I26:C(I)3::20100:1006 CH%61010$ :5,1855,5274,5274,1854,1854,5:275,5275,185:45,545,2546::C(0)3> R06:X%BOX(R,0):Y%BOX(R,1):C(R):40000::3] MN%0:MX%9:300:CH%1020 ::80:T0:I14:T(I)(36320I):TTT(I)::TĢ10:30000 :L124:L:40):::V519:V:5:32)::S$(1)"DISCUSSION":S$(2)"RULE":S$(3)"EXAMPLE":@21V3HI@Press [SPACE BAR] to Continue":16368,0D E10:KY32325^ H"@21V1H@"36)"@I@": hVS:ZZ1LN:HS:SP)"":ZZ: 35400,0 20000:BOX(6,1):(36309)İ2000 :R06:C01:BOX(R,C):C,R:31153,0:30100:11:I16:10:"["I"]":3 63900_EDU-WARE COPYRIGHT (C) 1982, 1984 EDUWARE SERVICES, INC. ALL RIGHTS RESERVEDv 24576:30719:999 KY(16384)128:ZZ(1):KY010 16368,0:P0:1002::,10:KY27KY480CH%KY48:CH%0CH%MX%30020 A"           p"p>1, >0>"><"">"","">> >"<,<"*" ">>*1,<Acx>``~x?> ><,<"*" ">" 0"  c`<`@x   p"p>"6<1, >0>"><"">"","">> >"<,<"*" ">>>1,<Ax>``~x?> ><,<"*" "> >>"8Yc~2 "" ""  >""""""2" "-"0""&2" *"", "*> A2*>~A>|>" ~>`0|xw>0"&2" *"", "*0>">"<E{>, >& > "" >>""2" "2"* ""-0"<&2>"*""&2""*](,~A>|" ~>x` xxxx0<&2>"*""&2""*?">"8RYo >* <0>"">**""""!0r &2"& *&"&2&""*?E ><A>|<<>x` pxxx0 &2"& *&"&2&""*0>">p"p>R"c~> 2 "" >"""" *&""""""!"0>,,<>"""">]  6A>|>"" >`0`x>0",,<>"""">TULATIONS! YOU HAVE PASSED@D3H@UNIT ONE AND MAY NOW GO ON TO UNIT@D3H@TWO.":W2ĺ"@8H18V@ARROW SHOWS AREA OF WEAKNESS"%5509%"@I5H17V@ARROWS SHOW AREAS OF WEAKNESS"&&"@I@":321:31051:20000:20100:1100f&'X,YHX,YXL,X1,Y";:4:W(I)4PT(I):"@2D3H@"CH$(I)"@22H@"PT(I)"@5F@"W(I);:W(I)1ĺ"@I4F138K15C@<--@0KI@";:WW1(%I:CH$(2)"COMMUTATIVE;ASSOCIATIVE":CH$(3)"IDENTITY;DISPLACEMENT":CH$(4)"OPPOSITE":WW1:W5506,5506,5508,5508,5508%21,127258,127:"@I16V3H@C213717841:X2,60X2,124X21,124X21,60:X2#~"@I6V3H@"34)"@6V8H@CONCEPT@6V20H@RIGHT WRONG ":21,47258,47:SP5:LN13:HS33:VS7:360:HS4:VS17:LN3:SP32:3609$CH$(2)"ASSOCIATIVITY":CH$(3)"IDENTITY ELEMENT":CH$(4)"OPPOSITES"$W0:@V7H@CORRECT":PT(2)PT(2)1:5232"n"@18V3H@NO. ANSWER IS ";QU"p321"qVS13:SP17:360:VS13:HS3:360:PPX4:3401:31051"PX4:4401:31051x#|X17:Y44:L246:H112:10000:Y60:L203:H64:10000:X2137:Y7610816:X,YX2,Y:Y:X"R1"@R15C@""j321:VS13:HS22:LN7:SP17:360:"@12V21H@WHICH AXIOM IS@D21H@REPRESENTED?@D21H@<1> SUBSTITUTION@D21H@<2> COMMUTATIVE@D21H@<3> ASSOCIATIVE@I18V21H@ WHICH (1-3)? @I@":147,143265,143i"lMN%1:MX%3:300:"@35H18V@"CH"@181HDENCE TRUE? @I@ @I@":MN%0:MX%9:300:"@I36H15V@"CH%"@I@":CH%R1ĺ"@26H17V@CORRECT":522 !d"@24H17V@INCORRECT-@D23H@ANSWER WAS "R1:321:"@15V@":ZZ12:"@D22H@"15):ZZ:LN7:52334!fQU1QU2ĺ"@8H15VL133C@"R1"@R15C@"X!hQU3ĺ"@2H15VL70,120,70,126_Ã-4,-4,70,136,70,142,-4,-4,70,152,70,158,-4,-4,-4,-4,37,52,49,52,91,52,98,52,-4,-4,-4,-4,70,39,70,77,70,93,70,109,70,125,70,141,70,157,-4,-4(222)255Ħ80:251,1:252,(222):253,(218):254,(219):(4)"RUNAM3.ERROR":259,78,59,94,59,110,59,126,59,142,59,158 ZÃ49,20,56,14,91,14,98,20,91,26,56,26,49,20,-4,-4,70,40,91,52,70,64,49,52,70,40,-4,-4,98,52,105,46,126,46,133,52,126,58,105,58,98,52,-4,-4,70,26,70,40,-4,-4,70,66,70,78,-4,-4,70,88,70,94,-4,-4,70,104,70,110,-4,-4,26,Y%10:3X%,Y%X%3,Y%3:X%,Y%X%3,Y%3:bX%,Y%X2%,Y2%:Y%Y2%ēX%1,Y%X2%1,Y2%v X%X2%:Y%Y2%::X%,Y%,X2%,Y2%:X%040270?X%,Y%X2%,Y2%:Y%Y2%ēX%1,Y%X2%1,Y2%D40250NX%,Y%:X%0ıS40100:40270'UÃ11,46,eset Menu@D20H@[0] Stop@I20V@";:G13:"@20H@"19)"":G:"@21V21H@Which ([0]-[9]) ?@I@"ouX%,Y%:X%040250uX2%,Y2%:X2%030108uX2%030108u40200:30110@X%,Y%X%25,Y%X%25,Y%10X%,Y%10X%,Y% TX%1,Y%X%1,Y%10:X%26,Y%X%25H@UNIT MENU@I2V8H@START@4D8H@MENU@15H@[0]@2H@[9]@26H6V@CONTENTS"u"@20HD@[1] Monomials@20HD@[2] Polynomials@20HD@[3] Simple@D24H@Factoring@20HD@[4] Factoring and@D24H@Binomials@20HD@[5] Quadratic@D24H@Trinomials@20HD@[6] PostTest"Xu"@20H17V@[9] R":11:"TO USE ANOTHER DISK"'3u30003~u275,5275,185:138,5138,185:137,5137,185:41,5637,5241,48:94,5698,5294,48u4,5276,5276,1854,1854,5:5,55,185:140,7272,7Bu"@I1V@";:Q13:"@20H@"19)"":Q:"@1V26H@ALGEBRA@D25H@VOLUME 3@D:(4)"CLOSE":35339:P*NX(36310):C(X)5:W3C(X)1:X6C(X1)3C(X1)6N80:(4)"UNLOCKAM3.PROGRESS":(4)"OPENAM3.PROGRESS":(4)"WRITEAM3.PROGRESS":I16:C(I)::(4)"CLOSE":(4)"LOCKAM3.PROGRESS":35339:0u10:"RESTART YOUR COMPUTERweak area)"@UN3ĺ"the PostestT. ";:Wĺ"(But 1 weak area)"o"@I@":321:20010:I3629936315:I,0::'X,YHX,YXL,YXL,YHX1,YHX1,Y:XL1,YXL1,YH: N80:X(36310):(4)"OPENAM3.PROGRESS":(4)"READAM3.PROGRESS":I16:C(I):"@I4F138K15C@"(29)(30)(31)"@0KI@";:WW1gI:W1ĺ"@I18V5H@Arrows show areas of weakness.":2040 21,127258,127:"@I16V3H@Congratulations! You have passed@D3H@";:UN6ĺ"Unit "UN" and may now go on to@D3H@";:UN4ĺ"Unit "UN1". ";:Wĺ"(But 1 6V3H@"34)"@6V8H@CONCEPT@20H@RIGHT WRONG ":21,47258,47:SP5:LN13:HS33:VS7:360:HS4:VS17:LN3:SP32:360W0:"@I8V@";:I16:PT(I)(36298I):CH$(I)Z$((36310),I):W(I)4PT(I):CH$(I)""2025+"@1D3H@"CH$(I)"@22H@"PT(I)"@5F@"W(I);:W(I)1ĺ ,10:KY27KY48: 0CH%KY48:CH%MN%CH%MX%300@ 2g 6KY(16384)128:GG(1):KY27ı 816368,0:"@40X40YN@"; :KY(16384)128:KY0314 ;16368,0:KY27Ĺ36309,0:80:(4)"RUNALGEBRA 3" <KY77Mı =319 >:318 m1 63900\AM3.1 COPYRIGHT (C) 1982, 1984 EDUWARE SERVICES, INC. ALL RIGHTS RESERVEDt 24576:30719:1000 310:KY010 16368,0:P0:1002::36312,C:X12:(36298X),NR(X)::36313,BG%:36314,EN%:IN$"-"IN$"-1"                CAA">"">>"><>">>">">">>0I):I:(4QU1,Y4V''QU:' N26:80:(4) OP N"F$:(4)"READ"F$:I15:C(I):I:C(1)5:W3C(1)1CAA">"">>"><>">>">">">>0I):I:(4F0I):I:(41:36:">":Y2:20:"0":X21:X2250:YY83:X,YX2,Y:YY1:X1:X,YX2,Y:YY2:X,YX2,YL''QU302407:QU,Y4QU,Y2QU1,Y2QU1,Y4:(QU30)35((QU30)35)ēQU,Y4QU,Y5QU1,Y51,Y4:(QU30)35((QU30)35)ēQU,Y4QU,Y5QU1,Y5QU1,Y4V''QU:' N26:80:(4) OP N"F$:(4)"READ"F$:I15:C(I):I:C(1)5:W3C(1)1CAA">"">>"><>">>">">">>:31051:20000:20100:1100f&'X,YHX,YXL,X1,YHX1,Y:XL1,YXL1,YH:&'Y1:4:"<":Y1:36:">":Y2:20:"0":X21:X2250:YY83:X,YX2,Y:YY1:X1:X,YX2,Y:YY2:X,YX2,YL''QU302407:QU,Y4QU,Y2QU1,Y2QU1:W5506,5506,5508,5508,5508%21,127258,127:"@I16V3H@CTULATIONS! YOU HAVE PASSED@D3H@UNIT ONE AND MAY NOW GO ON TO UNIT@D3H@TWO.":W2ĺ"@8H18V@ARROW SHOWS AREA OF WEAKNESS"%5509%"@I5H17V@ARROWS SHOW AREAS OF WEAKNESS"&&"@I@":321":CH$(3)"IDENTITY ELEMENT":CH$(4)"OPPOSITES"$W0:@";:4:W(I)4PT(I):"@2D3H@"CH$(I)"@22H@"PT(I)"@5F@"W(I);:W(I)1ĺ"@I4F138K15C@<--@0KI@";:WW1(%I:CH$(2)"COMMUTATIVE;ASSOCIATIVE":CH$(3)"IDENTITY;DISPLACEMENT":CH$(4)"OPPOSITE":WW:X2137:Y7610816:X,YX2,Y:Y:X213717841:X2,60X2,124X21,124X21,60:X2#~"@I6V3H@"34)"@6V8H@CONCEPT@6V20H@RIGHT WRONG ":21,47258,47:SP5:LN13:HS33:VS7:360:HS4:VS17:LN3:SP32:3609$CH$(2)"ASSOCIATIVITY"0VE 0ADDITION T"T" caacCcAA;: 019 080 Y4V''QU:' N26:80:(4)"OPEN"F$:(4)"READ"F$:I15:C(I):I:C(1)5:W3C(1)1:C(2)3C(2)6'*N(4)"CLOSE":3 04) 0I):I:(4SE":(4)"LOCK"F$:35339:(PÃ" HX1,Y:XL1,YXL1,YH:&'Y1:4:"<":Y1:36:">":Y2:20:"0":X21:X2250:YY83:X,YX2,Y:YY1:X1:X,YX2,Y:YY2:X,YX2,YL''QU302407:QU,Y4QU,Y2QU1,Y2QU1,Y4:(QU30)35((QU30)35)ēQU,Y4QU,Y5QU1,Y5QU1,$"@L15C@IF":A$"@L15C@AND":T$"@L15C@THEN":Q$(1)"@R15C2H15V@THE NUMERICAL COEFFICIENT IS":Q$(2)"@R15C2H15V@THE POWER OF "I14:CH$(I)::MO$"monomial":(36309)2BG%1:EN%2:R1:3400:36299,NR(1):80:(4)"RUNAM3.2":PL36309,0:C0:P0:M0:age@3H22V@Press ["(2)"] to View the Last Page@I@"Q10:KY8İ922:PP1:1220mKY21İ920:PP1:1220v932(36)2):X(36)73:Y(37)82:HD$" ";:L(HD$)76:H11:10000|35339:CH$(4),MN(6),MN$(5),VT$(4),SV%(4):R(I)((1)I):I0)703KY89KY121CG1C"@I21V1H@"38)"@D1H@"38)"@I@":c"@1H1V@C"C" P"P"@D1H@M"M:"@I2V7H@"31):24(HD$)2:HD$"@I@":31051:92430976"@21V1HI@"38)"@D1H@"38)"@I@":2"@3H21VI@Press ["(1)"] to View the Next P4H17V@"A$(1)V$(1)"@R15C@"A$(2)"@L138C@"V$(2)"@R15C@"A$(3):e "@R15C18V@";:IA$AA$ĺ"@12H@";:512 "@2H@No. Answer is @U@";:X7:S1:E0:450CG0:"@21V2HI@Do You Want to Change Your Answer?@D16H@[Y or N]@I@"10:(KY89KY121KY78KY11362:I26:444::N%(4)R(8)2:N%(1)N%(4)N%(7):S0:X1:"@L12H5V@";:450jN%(XZ)ĺ"@R15C@"N%(XZ);p"@9H18VR@";:IA$AA$ĺ"No@23H12V@= "AM$:"Right":NR(R)NR(R)1:434:"@R15C11H15V@";:IA$AA$512;"No. Answer is:@L138C2:BX%2:BY%9:BH%10:BW%18:360:BX%22:BW%16:360KN%(XZ)FV$(X)"1"QdFV$(X)V$(X):X12:N%(X7)N%(X1)N%(X4)::"@IR@":BX%2:BY%5:BW%36:BH%H:360362:I18:N%(I)R(2)2::X1:"@L2H12V@";:S0:410:439K472:X12:FV$(X)V$(X):(N%(X1)N%(X4))462gZ1:466:"@L10C22H"102X"V@"FV$(X);:470:486"@L138C@/";:Z4:466:"@L10C@"FV$(X);:470:486"@L138C@=";:Z7:466:"@10C@"FV$(X);:486:"@R15C@":2BX%12:BY%5:BH%2:BW%25:360X12:149X,H149X,156::H60N%(7)R(9)18a"@L10C@"N%(X);:Y12:N%(XY)452"@L10C@"V$(Y);:N%(XY)ĺ"@R15C@"N%(XY);:SS1:"@L138C@/";:X4:450Eĺ"@L138C@=";:HT%(36)1:X12:"@L10C@ "V$(X);:"@R15C@":3$BX%2:BY%11:BH%8:BW%36:360CX13:A$(X)""::AA$"":IA$"":434:Q$(1):MX%2:F2:VB%18:HT%5:350:434:Q$(2)V$(1)" IS":F1:HT%13:350:434:Q$(2)V$(2)" IS":HT%18:350:700:CG440428:516:321:438N%(I)R(4)1R(2):2:N%(X3)1ĺ"@R15C@"N%(X3);8N%(5)SX5:S1:410g"@L10C10H17V@"V$(1)"@15H@"V$(2)"@R15C@":X23:N%(5)1A$(X)A$(X)(N%(X)N%(4)N%(X4)N%(8)):432A$(X)A$(X)(N%(X)N%(4)):X13:AA$AA$A$(X)::"@R15C2H15V@"30):VT%(3)2390368-3:14,39265,39:cX1N%:"@L10C"Y"V"H4X"H@"V$;:XN%ĺ"@138C@*"u:"@R15C@":"@R15C2H15V@"30):"@L15C@(";:N%(X)1ĺ"@10C@"N%(X);Y12:"@L10C@"V$(Y);:N%(XY)1ĺ"@R15C@"N%(XY);:"@L15C@)";"-"VT$(X):386,AM$AM$(SV%(X))VT$(X)NXVT%SV%(X1)0AM$AM$"+"V:VT%0:X13:VT%(X)0:SV%(X)0::362:NTR(3)2:X1NT:366:Q%R(3)1:MN$(X)V$(Q%):VT%(Q%)VT%VT%1:VT$(VT%)V$(Q%) VT%(Q%)VT%(Q%)1::VT%(1)2VT%(2)2"(":S0:Y1NT:MN$(Y)VT$(X)SV%(X)SV%(X)MN(Y):SMN(Y)0GM$GM$"+"q vMN$(Y)VT$(X)GM$GM$(MN(Y)):S1 xY:GM$GM$")"VT$(X):XVT%GM$GM$"+" zX |AM$"":X1VT%:SV%(X)Ă: ~SV%(X)1AM$AM$VT$(X):386SV%(X)1AM$AM$Ⱥ"@"BX%"H"BI"V@"BW%)::U jX12:V$(X)("AEMNRTXY",R(8)1,1)::V$(1)V$(2)362m lV$(3)V$(1)V$(2): nMN(X)(R(8)2)1R(2): pPM$"":Y1X1:IM$(MN(Y))MN$(Y):MN(Y1)0YX1IM$IM$"+" rPM$PM$IM$:I tGM$"":X1VT%:GM$GM$F:1):KY13PS%3597 c(KY8KY127)PS%PS%PS%1 e(KY47KY58KY45PS%)PS%MX%ĖHT%PS%F:(KY);:256PS%,KY:PS%PS%1 f352 gIN$"":I0PS%1:IN$IN$((256I))::260:IN(IN$):IN$(IN):"@R@":IA$IA$IN$: hBIBY%BY%BH%1: ?63900% @"@R15C0K@":922:1200_ A"@21V3HI@Press [SPACE BAR] to Continue@I@":16368,0s E10:KY32325 H"@I21V1H@"36)"@I@": ^F2ĺ"@L@" _VB%:HT%:MX%):PS%0:I0MX%:256I,32::16368,0 `HT%PS%F:"@I@ @I@";:10:HT%PS%H15V@= @15C@(@10C@2@138C@*@10C@3@15C@)(@10C@X@24H@X@27H15C@)(@10C@YY@36H15C@)@5H17V138C@= @10C@6X@16H@Y@138C23H@=@10C26H@6X@31H@Y@R15C23H15V@2@2F@3@8F@2@2D13H@2+3@2F@1+2@30H@5@2F@3":930*: "@1H5V@This rule does ";:HD$"not":940:" apply to the@2D1H@proe factors.":930(0 "@1H5V@To multiply "MO$"s, you may use@2D1H@this exponent rule as well as the@2D1H@Commutative and Associative Axioms of@2D1H@Multiplication. For example@7H13V@2@18H@3 2@1H13VL@(@10C@2X@8H@Y@15C@)(@10C@3X@19H@Y@22H15C@)")2 "@138C5@*@10C@X@138C10H@=@15C@(@10C@X@138C@*@10C@X@138C@*@10C@X@15C@)(@10C@X@138C@*@10C@X@15C@)"(( "@10H11V138C@= @10C@X@138C19H@= @10C@X@R16H15C@5@25H@3+2@1H14V@When you multiply two powers of the@2D1H@same base, keep the base and add the@2D1H@exponents of th50::700:CG2416@&r 510:321:"@9H18V@"10)::920:C11200F&t a& M3100,3200,3300,3400& P3110,3120,3130,3140,3150,1200Y'& "@14H5V@3@L12H10C@X@15H138C@=@10C@X@138C@*@10C@X@138C@*@10C@X@15C@,@5V1H@SINCE@29H@THEN@R4H8V@3@4F@2@L2H10C@X@5H138Cm's numerical@D2H@coefficient below.":LBG%EN%:PL:900:"@7H12V@"30)"@4H17V@"20)r%m 390:VT%1SV%(1)2413%n "@7H12V@"PM$:439:X1VT%:AA$AA$(SV%(X)):"@17V"7X1"H@"VT$(X);:XVT%ĺ"+"%o &p IA$"":F1:MX%3:VB%18:X1VT%:HT%7X2:3D6H@the numerical@D6H@coefficients":930$` H4:476:Y36:H39:9999:396:"@2H5V@Use the Distributive Axiom of@D2H@Multiplication to add and subtract@D2H@all like "MO$"s in the problem@D2H@below."U%l Y84:H72:9999:"@I2H11V@Add@4D2H@and enter each ter1200;# Y36:H16:9999:H120:9999:"@2H5V@ADD":H52:446T# 390:(GM$)162312($ "@6H5V@"PM$"@3H8V@1) State problem@22H@"PM$"@3H2D@2) Group numerical@22H@"GM$"@D6H@coefficients@D6H@with@D6H@Distributive@D6H@Axiom@3H2D@3) Add or subtract@22H@"AM$"@ coefficients""Y108:H40:9999:"@2H10V@and multiply this sum by the common@D2H@variable factors.@3D2H@To subtract one "MO$" from@D2H@another like "MO$", add the@D2H@opposite (additive inverse) of the@D2H@subtrahend to the minuend.""930#P3 variables will@2D1H@remain the same.":930"@R15C1H5V@An expression that is the product or@2D1H@quotient of numeraLGEBRA 3":$jHD$CH$(C):910:920?tC1200,1200,4000,5000P0:M0:900:"@12H5V@LEARNING MODES@2D4H@[1] Discussion@2D4H@[2] Rule@2D4H@[3] Example@2D4H@[4] Sample Problem@2D4H@[0] Return to Concept Menu@6D5HI@Which ([0]-[4]) ??@I@"MN%0:MX%431,9831,11028,107:32,9832,11035,107:59,3259,15960,15960,32["@14V3H@[0]@20H5V@CONCEPTS@10H12V@[0] Return to Unit Menu@9DI11H@Which ([0]-[4]) ??@I@":X14:"@10H"6X"V@["X"] "CH$(X):NR(X)0: eMN%0:MX%4:300:CCH%:Cİ922:80:(4)"RUNA900:HD$"":910:X18:Y388616:H12:L27:10000:(Y10)8:"@3H@["(Y22)16"]"VY86ēX13,Y12X13,Y16:X10,Y13X13,Y16:X14,Y12X14,Y16X17,Y13DX:21,12214,11621,11042,11049,11642,12220,12213,11620,110:43,11050,11643,122:on,Monomial Test"9(222)255Ħk980:251,2:252,(222):253,(218):254,(219):(4)"RUNAM3.ERROR":PUNAM3.ERROR":PPROR":PP21200 8z +8200:80:(4)"RUNAM3.1.1":~8I13:NR(I)0::P0:M0:BG%1:EN%4:R1:2400:R2:3400:BG%1:EN%4:R3:40008'X9:L2628'X,YHX,YXL,YXL,YHX1,YHX1,Y:XL1,YXL1,YH:9PÃAddition and Subtraction,Multiplication,Divisi440:c7X L34:PL:900:478:N%(2)1:N%(3)1:N%(5)0:480:A$(1)(N%(1)N%(4)):440::BG%5:EN%67Z LBG%EN%:PL:900:478:N%(5)0:480:A$(1)(N%(1)N%(4)):440:7\ LEN%1EN%2:PAL:900:478:N%(5)1:N%(1)1:480:A$(1)"1":440:8y 920:C2h expression and then@D2H@enter the numeric factor and the@D2H@power of each variable factor."6T "@I2H10V@WHEN YOU SIMPLIFY THIS EXPRESSION":C4BG%1:EN%2:34186U (36309)234187V L12:PL:900:478:N%(4)1:N%(8)1:480:A$(1)(N%(1)N%(5)):)"E5 N%N%(2):Y14:H3:V$(N%(1)):400:H13:V$V$(1):N%(2)3H175 400:"@L10C5H17V@"N%(1)"@R15C@"N%(2)"@L10C17V@"V$"@R15C@"N%(2)"@L10C14H17V@"(N%(1)N%(2))V$"@R15C@"N%(2):930^6H Y36:H32:9999:Y76:H80:9999:396:H3:476:"@2H5V@Simplify eac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u1e integers I and J,@2D17H@I J@5F@I*J@L13H10V@(@10C@X@15C18H@)@138C21H@=@10C24H@X@R15C@":930x/ P3310,3318,3324,1200/ N%(1)R(4)1:N%(2)R(4)1:N%(1)N%(2)7N%(1)N%(2)3310[0 362:V$V$(1):"@1H4V@"I$"@10C6H@"V$"@138C9H@=@R15C8H4V@"N%(1):N%N. "@R15C2H13V@Rule of Exponents for a Power of a@D16H@Product@2D2H@For every integer I,@D2B@I@4F@I I@L12H17V@(@10C@XY@15C@)@138C21H@=@10C@X@26H@Y@R15C@":930]/ Y36:H64:9999:"@3H5V@Rule for Exponents for a Power of a@D18H@Power@2D2H@For all positiv(2+2+2=6) or by multiplication@2D1H@(2*3=6).":930H- P3210,3220,1200- Y36:H56:9999:Y100:9999:"@2H5V@Rule of Exponents for Multiplication@2D2H@For all positive integers I and J,@2D15H@I@4F@J@4F@I+J@13H9VL10C@X@138C16H@*@10C@X@138C21H@=@10C@X"@power.":930,N "@L12H5V@(@10C@X@17H15C@)@138C20H@=@10C@X@25H@X@28H@X@11H8V15C@(@10C@X@16H15C@)@138C19H@=@10C@X@15C1H5V@SINCE@R16H@2@2F@3@4F@2@2F@2@2F@2@D@,@L1H8V@THEN@R15H@2@2F@3@4F@6@D@. The exponent@2D1H@can be found either by addition"2-P "@1H13V@ not equal since@11F@is@L17H5V10C@2X@27H15C@(@10C@2X@15C@)@21H8V@(@10C@2X@15C@)@1H11V@(@10C@2X@15C@)(@10C@2X@15C@)@138C@=@20H10C@4X@R15C24H@2@D@. When finding" ,F "@1H14V@the power of a product, you must raise@2D1H@each factor in the product to that@2D1Hduct of powers of different bases.@3D1H@You can ";:940:" simplify@U3F@2 3@D@, because@3D1H@the base@4F@is different from the base"*< "@L23H9V10C@X@26H@Y@10H12V10C@X@1H15V@Y@15C@.@R@":930+D "@1H6V@The two numbers@U5F@2@D@ and@U9F@2@3D29H@2@D1H@areN%(XZ);$AI075:310::;AI0100:310::^700:"@9H18V@";:IA$AA$514~"@R@RIGHT":NR(R)NR(R)1:"@R@WRONG@23H12V@= "AM$:434:700:"@R15C11H15V@";:IA$AA$512&"@R@WRONG, ANSWER IS:@L138C24H17V@"A$(1)V$(1)"@R1X12:N%(X7)N%(X1)N%(X4)::2PL:900\"@IR@":BX%2:BY%5:BW%36:BH%H:360u362:I18:406::X1:"@L2H12V@";:S0:410:439362:I26:444::I4:404:N%(1)N%(4)N%(7):S0:X1:450922:1200N%(XZ)0ĺ"@R15C@"5"@L138C@/";:Z4:466:"@L10C@"FV$(X);:470:486d"@L138C@=";:Z7:466:"@10C@"FV$(X);:486v:"@R15C@":BX%12:BY%5:BH%2:BW%25:360:BX%2:BY%9:BH%10:BW%18:360:BX%22:BW%16:360N%(XZ)0FV$(X)"1"FV$(X)V$(X):%0C@"V$(Y);:N%(XY)0ĺ"@R15C@"N%(XY);L:SS1:"@L138C@/";:X4:450Eĺ"@L138C@=";:HT%(36)1:X12:"@L10C@ "V$(X);:"@R15C@":472:X12:FV$(X)V$(X):N%(X1)0N%(X4)0462Z1:466:"@L10C22H"102X"V@"FV$(X);:470:4862:HT%5:VB%17:350u434:F1:VB%18:HT%13:Q$(2)V$(1)" IS":350:434:HT%18:Q$(2)V$(2)" IS":350:516:321:438N%(I)R(4)1(R(2)):X12:149X,H149X,156::H60N%(7)R(9)1"@L10C@"N%(X);:Y12:N%(XY)0452("@L1X23:N%(5)1A$(X)A$(X)((N%(X)N%(4))(N%(X4)N%(8))):432aA$(X)A$(X)(N%(X)N%(4)):X13:AA$AA$A$(X)::"@R15C2H15V@"30):BX%2:BY%11:BH%8:BW%36:360X13:A$(X)""::IA$"":AA$"":Q$(1):428:MX%3:FG0:FR(2)2:""@R15C2H15V@"30):J"@L15C@(";:N%(X)1ĺ"@10C@"N%(X);Y12:"@L10C@"V$(Y);:N%(XY)1ĺ"@R15C@"N%(XY);:"@L15C@)";:N%(X3)1ĺ"@R15C@"N%(X3);N%(5)SX5:S1:410"@L10C10H17V@"V$(1)"@15H@"V$(2)"@R15C@":B)V$(Q%):VT%(Q%)0VT%VT%1:VT$(VT%)V$(Q%)eVT%(Q%)VT%(Q%)1::VT%(1)2VT%(2)2VT%(3)2390n3683:14,39265,39:N%(I)R(4)1:X1N%:"@L10C"Y"V"H4X"H@"V$;:XN%ĺ"@138C@*":"@R15C@":N%(I)R(8)2: N%(I)AM$"":X1VT%:SV%(X)Ă:>~SV%(X)1AM$AM$VT$(X):386eSV%(X)1AM$AM$"-"VT$(X):386AM$AM$(SV%(X))VT$(X)XVT%SV%(X1)0AM$AM$"+":-VT%0:X13:VT%(X)0:SV%(X)0:X:362:NTR(3)2:X1NT:366:Q%R(3)1:MN$(XY))MN$(Y):MN(Y1)0YX1IM$IM$"+"9 rPM$PM$IM$: tGM$"":X1VT%:GM$GM$"(":S0:Y1NT:MN$(Y)VT$(X)SV%(X)SV%(X)MN(Y):SMN(Y)0GM$GM$"+" vMN$(Y)VT$(X)GM$GM$(MN(Y)):S1 xY:GM$GM$")"VT$(X):XVT%GM$GM$"+" zX|$"":I0PS%:IN$IN$((256I)):I:IN(IN$):"@R@":IA$IA$IN$:u hBIBY%BY%BH%1:"@"BX%"H"BI"V@"BW%):BI: jX12:VR(6)84:V$(X)(V)::V$(1)V$(2)362 lV$(3)V$(1)V$(2): nMN(X)(R(9)1)1(R(2)):' pPM$"":Y1X1:IM$(MN(352@ a250:HT%PS%F:((256PS%));:KY155ESC%1:"@R@":T bKY141PS%359n cKY136PS%PS%PS%1 dKY149PS%MX%PS%PS%1 eKYKY128:(KY47)(KY58)(KY45PS%0)ĖHT%PS%F:(KY);:256PS%,KY:PS%PS%1:PS%MX%359 f351C gIN"@22V1HI@..PRESS (SPACE BAR) TO CONTINUE...":250H C310:KY128323^ E250:KY160323x H"@22V1H@"36)"@I@": ^VB%:HT%:MX%):PS%0:I0MX%:256I,32:I:16368,0:F2ĺ"@L@" _HT%PS%F:"@I@"((256PS%))"@I@"; `310:KY128KY149CH%MN%CH%MX%300 2C 6GG(1):KY(16384):290:KY155ıZ 8250:"@40X40YN@";| :KY(16384):290:KY128314 ;250:KY155Ĺ36309,0:26:(4)"RUNALGEBRA 3" <KY205Mı =319 >:318 ?63900 @"@R15C0K@":922:12003 A524576:30719:63900(AM3.1.1lCOPYRIGHT 1982 EDU-WARE SERVICES, INC. ALL RIGHTS RESERVED F$"AM3.PROGRESS":10000:1002P::16368,0:"XXR(1):,310:KY128300.250:KY155CH%0 0CH%KY176:                    &B"@11H4V@3@25H@2@2D16H@1@30H@-2@6F@.@2D11H@2@25H@4@36H@2@3D1H@Multiplying them all together we get@5H13V@3@2F@2@4D5H@2@2F@4@16H@2":930&hP4210,4220,4230,1200c'rY36:H96:9999:"@L138C12H12V@$$ = $*$@10C12H10V@XY X Y@12H14V@CD C D@R15C10H5V@Pch@2D1H@part separately.":930%@"@L138C1H6V@$=@9H@$@12H@=@17H@=@23H@$@26H@=@32H@=$@1H15V@$$$$@10H@=@13H@$$@10C1H4V@4@9H@X@23H@Y@34H@1@5H6V@2@14H@X@19H@X@28H@Y@1H8V@2@9H@X@23H@Y@34H@Y@1H13V@4X@6H@Y@13H@2X@1H17V@2X@6H@Y@14H@Y@15C7H6V@,@21H@,@R18H15V@."H@$*$@30H@*$@10C1H9V@4X@6H@Y@1H13V@2X@6H@Y@23H9V@4@F@X@32H@Y@23H13V@2@F@X@32H@Y"%8"@R15C1H5V@From our experience with fractions, we@2D1H@know that:@2D5H@3@2F@2@29H@3@4F@2@2D11H@is equal to@D5H13V@2@2F@4@29H@2@4F@4@3D1H@We can simplify it by dividing ea@3@7F@2@D7B@and@6F@are reciprocals.@L14H7V@SINCE@R8V@ the first@3H@2@7F@3@2D24H@1@D1H@fraction is equal to@4F@, and the@2D13H@-1@D@,@1H@second to@2DL1H@THEN@R21H@1@32H@-1@D10H@they are@D26H@-1@38H@1@D1H@reciprocals, too."#0930P$6"@L138C1H11V@$$$$@23ne, so@2D4H@Y@D8F@Y-Y@D8F@0@2D4H@Y@3D1H@Any number with a zero exponent is"l"$"@1H18V@equal to one.":930","@L138C1H6V@$@9H@$@22H16V@=$@34H@=$@10C1H4V@X@9H@X@1H8V@X@9H@X@22H10V@X@11H13V@X@24H14V@1@36H@1@19H16V@X@30H@X@24H18V@X@36H@X"#."@R15C3H4Vuotient is@2D1H@found by subtracting the divisor's@2D1H@exponent from the dividend's@2D1H@exponent."m!930K"""@L138C2H11V@$@7H@=@18H@=@27H@=@10C2H9V@X@11H11V@X@22H@X@31H@1@2H13V@X@R15C1H5V@We know that every nonzero number@2D1H@divided by itself is o2" "@L138C15H9V@*@20H@=@27H@=@10H14V@$@13H@=@20H@=@10C12H9V@X@17H@X@22H@X@29H@X@10H12V@X@15H14V@X@22H@X@10H16V@X@R15C@":930d!"@L10C15H5V@X@R15C@3 (EXPONENT)@2D13H@(BASE)@2D1H@When dividing two powers with the same@2D1H@base, the exponent of the q,7000 M4100,4200,4300,4400JP4110,4120,4130,4140,4150,4160,1200 "@R15C1H5V@Division and multiplication are said@2D1H@to be inverse operations of the other.@2D14H@2@4F@3@4F@2+3@4F@5@D@,@U1HL@SINCE@1H14V@THEN@R12H12V@5@2D4F@5-2@4F@3@D@.@D12H@2D4H@<4> SAMPLE PROBLEM@2D4H@<0> RETURN TO CONTENTS@6D5HI@WHICH ONE (0-4) ??@I@"MN%0:MX%4:300:CH%İ922:26:(4)"RUNAM3."(36310)P1:MCH%:920:36320M,(36320M)(36320M)255P1200900:(36310)1ĴC24000,5000C26000T$"@L15C@THEN":BG%(36313):EN%(36314)xMO$"monomial":P$"polynomial":C$"coefficient":V$"variable":N$"numeric"LC(36312):P0:M0:900tC4ī1225PP0:M0:900:"@12H5V@MODE SELECTION@2D4H@<1> DISCUSSION@2D4H@<2> RULE@2D4H@<3> EXAMPLE@310:KY1289314250:KY136İ922:PP1:1220QKY149İ920:PP1:1220Z931(36)2):X(36)73:Y(37)82:HD$" ";:L(HD$)76:H11:10000)35339:CH$(4),MN(6),MN$(5),VT$(4),SV%(4):R(I)((1)I):I$"@L15C@IF":A$"@L15C@AND":1$:AA$T2$:,"@1H1V@C"C" P"P"@D1H@M"M:X"@I2V7H@"31):24(HD$)2:HD$"@I@":h31051:924s30976"@21V1HI@"38)"@D1H@"38)"@I@":"@5H21VI@PRESS "(1)" TO VIEW THE NEXT PAGE.@3H22V@PRESS "(2)" TO VIEW THE PREVIOUS PAGE.@I@""@R@":BX%22:BY%8:BH%11:BW%16:360:K5:X01:B,VXE,VX::3:ZNP1ĺNP;jNP1ĺ" ";vVA$;:T1$"":T2$"":IY1(IA$):(IA$,IY,1)" "T1$T1$(IA$,IY,1):IY1(AA$):(AA$,IY,1)" "T2$T2$(AA$,IY,1) :IA$Tdend.":r"@R22H8V@If the remainder@D23H@is greater than@D23H@or equal to the@D23H@divisor it is@D23H@the new@D23H@dividend.":w"@I13H14V@"N(6)V$"+"N(4)"@23H13V@"N(6)"("V$"+"N(1)")=@23H16V@"N(6)V$"+"N(8):500BX%1:BY%4:BH%16:BW%20:360)@"N(4)" @R15C@":$NN(I1)R(2)17XN(I)R(9)1:l"@R22H8V@Divide left term@D23H@of the dividend@D23H@by left term of@D23H@the divisor.":n"@R22H8V@Multiply divisor@D23H@by the@D23H@quotient.":p"@R22H8V@Subtract product@D23H@from divi5C@"A$(2)"@L138C@"V$(2)"@R15C@"A$(3):e "@R15C18V@";:X13:(TA$(X))(AA$(X))Ă:"@12H@";:512 "@2H@WRONG, ANSWER IS @U@";:X7:S1:E0:450700:"@R15C11H17V@";:IA$AA$512"WRONG, ANSWER IS":505:"@L138C11H11V@ "N(3):505:"@19H11V8H7V@"VP$"+"N(3)V$"+"N(4)"@8H9V@"VP$"+"N(5)V$:505:"@I13H12V@"N(6)V$"+"N(4)"@23H11V@"VP$"+"N(3)V$"+"N(4)"-@23H14V@("VP$"+"N(5)V$")=@23H17V@"N(6)V$"+"N(4):500?7"@L8H7V@"VP$"+"N(3)V$"+"N(4)"@8H9V@"VP$"+"N(5)V$:500:652:626:500:652:620:"@IL1H7V@"V8C@=@15C@"V$:500:"@L1H7V@"V$"@8H@"VP$5500:652:622:505:"@IL1H7V@"V$"+"N(1)"@8H4V@"V$:505:"@I8H9V@"VP$"+"N(5)V$"@23H13V@"V$"("V$"+"N(1)")=@23H16V@"VP$"+"N(5)V$:500:"@L1H7V@"V$"+"N(1)"@8H4V@"V$6500:652:624:505:B56:V92:E144:660:"@LI2)963024VP$V$"@R@2@L@":N(3)N(1)N(2):N(4)N(1)N(2):N(5)N(3)N(2):N(6)N(3)N(5):"@L1H7V15C@"V$"+"N(1)"@8H@"VP$"+"N(3)V$"+"N(4):620:505'5"@IL1H7V@"V$"@8H@"VP$:505:"@IL8H4V@"V$:B161:V123:E174:660:"@L23H13V@"VP$"@23H16V@"V$"@L25H15V136H@remainder is less than the@D6H@divisor.":9303X150:Y36:H120:L119:10000:"@R15C22H5V@TO DIVIDE THESE@D22H@TWO POLYNOMIALS":L14:650:474:362:V$V$(1):B52:V51:E144:660:5:X12:51X,5251X,72::3 4I12:600::N(1)N(2)9N(1)N(the first term of@D6H@the divisor. The quotient is the@D6H@next term in the answer."03D"@2H12V@<3> Multiply the divisor by the new@D6H@term.@D2H@<4> Subtract the product from the@D6H@dividend to get a new dividend.@D2H@<5> Go back to Step 2 unless the@De as you would in long@2D2H@division until the remainder is less@2D2H@than the divisor.":930n18P6210,1200T2BY36:H120:"@6H5V@TO DIVIDE TWO POLYNOMIALS@2D2H@<1> Arrange both in descending order.@D2H@<2> Divide the first term of the@D6H@dividend by owers of a "V$",@2D2H@write them in with a zero ";0C$"@L6H17V10C@X@R15C@2@L138C@+@10C@3 @138C@= @10C@X@R15C@2@L138C@+@10C@0X@138C@+@10C@3@R15C@":930]1"@2H5V@Divide the first term of the divisor@2D2H@by the first of the dividend. Then@2D2H@continuerms by the "MO$".@3D2H@POLYNOMIAL = MONOMIAL + MONOMIAL"B/93020"@2H5V@To divide one "P$" by another@2D2H@we must use long division. First,@2D2H@arrange the terms of the dividend and@2D2H@divisor in decreasing order. If there@2D2H@are any missing p26:(4)"RUNALGEBRA 3"2.pM6100,6200,6300,6400M.P6110,6120,6130,12009/"@R15C2H5V@You have been told how to divide one@2D2H@"MO$" by another. You can divide@2D2H@a "P$" by a "MO$" in much@2D2H@the same way. Just divide each of the@2D2H@"P$"'s t@";:482:VB%15:MX%1:F2:350:TA$(1)IN$-@MX%2:F1:HT%HT%4:VB%16:350:TA$(2)IN$:HT%HT%4:350:TA$(3)IN$:472:X13:AA$(X)(N%(X6))::522-a321:BX%2:BY%15:BH%4:BW%36:360:L:C3ī484-b-R3:4400.922:36309,1:36301,NR(3):enter the quotient.",<"@2H8V@Then divide each variable factor and@D2H@enter the exponent of the quotient.@I3D2H@Perform the division and fill in@D2H@the missing portions of the answer.")->LBG%EN%:474:X13:TA$(X)""::N%(7)R(9)1:E1:"@L2H15V17V@3) Multiply all of@D5H@the quotients@UL22H@";:X7:S1:E0:"@22H17V@";:450o+"@R15C@":321:464:L:484,0Y36:H48:9999:Y92:H64:9999:396:H5:476:"@R15C2H5V@Divide the two "MO$"s displayed@D2H@below. Divide the numeric@D2H@coefficient and 60:446:E0:"@L12H5V@";:482*500:"@2H9V@1) Divide numeric@D5H@coefficients@UL22H10C@"N%(1)"@138C@/@10C@"N%(4)"@138C@=@10C@"N%(7):500*"@R15C2H12V@2) Divide variable@D5H@factors that@D5H@are powers with@D5H@the same base":456:500O+"@R15C2H3H@1@2H14V@A@17H@A@7H16V@A@23H@A@R15C4H5V@0@D5F@for every real number")"@2H9V@For all nonzero real numbers A and@D2H@all real numbers X,@4H14V@X@7F@and@4F@-X@2D9H@-X@25H@X":930*Y36:H24:9999:Y60:H96:9999:"@R15C2H6V@TO DIVIDE":L14:474:HH@For all positive integers I and J,@D2H@and nonzero real numbers A,"(~"@2H10V@IF I>J THEN@7F@IF I:318 ?63900 @"@R15C0K@":922:1200 A"@22V1HI@..PRESS (SPACE BAR) TO CONTINUE...":250 C310:KY12$(3)"XY":V$(5)"Y":V$(7)"Y@R15C@2":V$(9)"X":H(1)2:H(3)9:H(5)17:H(7)23:H(9)30:X192:V11r 16368,0: "XXR(1): ,310:KY128300 .250:KY155CH%0 0CH%KY176:CH%MN%CH%MX%300 2 6GG(1):KY(16384):290:KY155ı324576:30719:63900&AM3.2jCOPYRIGHT 1982 EDU-WARE SERVICES, INC. ALL RIGHTS RESERVED F$"AM3.PROGRESS":10000:1002P::36312,C:X12:(36298X),NR(X)::36313,BG%:36314,EN%:b AA$"":V$(1)"X@R15C@2":V                 : AM3.1.1":PP5:W3C(1)1:C(2)3C(2)67<*N(4)"CLOSE":35339:l"@R15C1H5V@A group of "M$"s joined by the@2D1H@operations of addition and "S$"ion@2D1H@is called a ";:HD$P$:940:". A "P$"@2D1H@made up of only two terms isSELECTION@2D4H@<1> DISCUSSION@2D4H@<2> RULE@2D4H@<3> EXAMPLE@2D4H@<4> SAMPLE PROBLEM@2D4H@<0> RETURN TO CONTENTS@6D5HI@WHICH ONE (0-4) ??@I@"MN%0:MX%4:300:CH%İ922:1100P1:MCH%:920:36320M,(36320M)(36320M)255P1200900:X"V@<"X"> "CH$(X):NR(X)0:c`"@10H12V@<0> RETURN TO ALGEBRA MENU@9DI11H@WHICH ONE (0-4) ??@I@"eMN%0:MX%4:300:CCH%:Cİ26:30976:(4)"RUN ALGEBRA 3"jHD$CH$(C):910:920nC34000tC4P0:M0:1225P0:M0:900:"@12H5V@MODE 3,Y16:X14,Y12X14,Y16X17,Y13XY:21,12214,11621,11042,11049,11642,12220,12213,11620,110:43,11050,11643,122:31,9831,11028,107:32,9832,11035,107:4:15:"<0>"Z59,3259,15960,15960,32["@20H5V@CONTENTS":X14:"@10H"6"numeric":C$"coefficient"g(36309)2BG%1:EN%4:R2:3400:36300,NR(2):920:26:(4)"RUNAM3.3"L36309,0:C0:P0:M0:900:HD$"":910:X18:Y388616:H12:L27:10000:(Y10)8:"@3H@<"(Y22)16">"%VY86ēX13,Y12X13,Y16:X10,Y13X1931N(36)2):X(36)73:Y(37)82:HD$" ";:L(HD$)76:H11:1000035339:R(I)((1)I):BG%1:EN%9:N(19),M(2,2),HP(2,2),VA$(2,2),P(2,2),P$(2,2):FG0:F2I14:CH$(I):I:M$"monomial":P$"polynomial":S$"subtract":V$"variable":N$":31051:92430976D"@21V1HI@"38)"@D1H@"38)"@I@":"@5H21VI@PRESS "(1)" TO VIEW THE NEXT PAGE.@3H22V@PRESS "(2)" TO VIEW THE PREVIOUS PAGE.@I@"310:KY128931250:KY136İ922:PP1:1220KY149İ920:PP1:122025:H(4)34:"WRONG, ANSWER IS":I101:K101:382:ACAC1:AC4ĺ"@L138C"H(AC)"H17V@ @"H(AC)"H@"M(1,I)M(0,K);:K,I*"@"H(AC)"H17V@ @"H(AC)"H17V@"M(1,I)M(0,K)"@R15C@":"@1H1V@C"C" P"P"@D1H@M"M:"@I2V7H@"31):24(HD$)2:HD$"@I@T2$(AA$,IY,1)(:IA$T1$:AA$T2$:P 700:"@R15C11H18V@";:IA$AA$804m""RIGHT":NR(R)NR(R)1:$"WRONG, ANSWER IS":X192:382:"@L10C16V"H(X)2"H@"N(X10)"@R15C@"::&700:"@R15C17H15V@";:IA$AA$802|(AC0:H(1)3:H(2)15:H(3)84I42,7984K42,73:K"@R15C@":BX%2:BY%15:BH%2:BW%32:360:VNPıtNP1(VP$)NP$VP$:422NP$(NP)VP$NP$;:T1$"":T2$"":IY1(IA$):(IA$,IY,1)" "T1$T1$(IA$,IY,1):IY1(AA$):(AA$,IY,1)" "T2$H@wide and 3Y+2 units high.@2D8B@6Y+1@4D5H@3Y+2":X73:Y84:H40:L133:10000:382:"@14H9V@6Y 1":X12:139X,84139X,124:50< 382:"@8H11V@3Y@2D5H@ @D@2":73,104207,104:382:"@LE12H11V@18Y@R@2@L22H@3Y@13H13V@12Y@23H@2":382:"@ER1H16V@The tby a "M$"@2D1H@in the same way. We can also multiply@2D1H@two "P$"s by multiplying the@2D1H@first "P$" by each of the terms@2D1H@in the second.";.2 " Then add all of the@2D1H@products together.":930/: "@1H5V@Suppose this rectangle was 6Y+1 units@2D1142S,100:139S,Y139S,100:K,S:3:103S,Y103S,100:176S,Y176S,100:142S,Y142S,100:139S,Y139S,100-. "@L10H10V@8X@R@2@L26H@6X@R7H11V@2X@19H@+@22H@2X@2D11H@4X@27H@3":930.0 "@1H5V@The distributive axiom allows us to@2D1H@multiply a "P$" m of the smaller@2D1H@ones will be equal to the larger one.":380:"@12H11V@ @2D4F@ ",* S134:K34:K:103S,Y103S,100:176S,Y176S,100,+ 3:103S,Y:103S,100:176S,Y:176S,100:4:142S,Y:142S,100:139S,Y:139S,100:Kp-, 142S,Y00,3400"+ P3110,3120,3130,1200+& "@R15C1H5V@The area of a rectangle is equal to@2D1H@the product of its length and width.@4D12H@2X@2D4F@4X+3":X101:Y76:L77:H24:10000:380:"@1H15V@But we can break it into smaller"Y,( "@1H17V@rectangles. The su252,122X::3:"@L10C6H16V@"V$(1)"@138CL@+ @10C@"V$(3)"@138C@+ @10C@"V$(5)"@138C@+ @10C@"V$(7)"@138CL@+ @10C@"V$(9)"@R15C@"*r X192:MX%1:HT%3H(X):VB%17:F2:350::800*t "@R15C@":321:Y11:H8:408:L:C1İ922:1200* + M3100,3200,338C"V"V"H(X)"H@+@10C@"N(Y)V$(X):2416X)l N(Y)1ĺ"@L138C"V"V"H(X)"H@+ @10C@"V$(X):2416)m N(Y)1ĺ"@L138C"V"V"H(X)"H@- @10C@"V$(X):2416)n "@L138C"V"V"H(X)"H@"((N(Y)),1)"@10C@"((N(Y)),1)V$(X)}*p V13:Y:AA$AA$(N(X10))::5:X12:14,122X)23:H(9)30:X192:V11l(d IXX1:374::N(X10)N(X)N(X1):N(X10)9N(X)N(X1)0N(1)N(2)2404(f YXX1:N(Y)2416(h X3N(Y)1ĺ"@L10C"V"V"2H(X)"H@"N(Y)V$(X):2416(i X3N(Y)1ĺ"@L10C"V"V"4H(X)"H@"V$(X):2416$)j N(Y)1ĺ"@L13@2H5V@Add the "P$"s below by adding@D2H@or "S$"ing their like terms.@D2H@Then fill in the "N$"@D2H@"C$"s for one answer.@I@":Y84:H72:9999:LBG%EN%:378(b 386:V$(1)"X@R15C@2":V$(3)"XY":V$(5)"Y":V$(7)"Y@R15C@2":V$(9)"X":H(1)2:H(3)9:H(5)17:H(7("N(2)V$(2)"+"N(4)V$(2)")":380:"@2H13V@<3> Distributive@D6H@axiom of@8F@("N(1)O$N(3)")"V$(1)O$"("N(2)"+"N(4)")"V$(2)"@D6H@multiplication":380& "@2H16V@<4> Substitution@7F@"N(5)V$(1)O$N(6)V$(2)"@D6H@principle":321:404:L:922:1200'` H40:406:"@2H5V@"O$(N(0)0)% "@24H5V@"O$"@27H@"O$"@30H@"O$:382:"@2H7V@<1> Commutative@D6H@axiom of@8F@"N(1)V$(1)O$N(3)V$(1)O$N(2)V$(2)O$N(4)V$(2)"@D6H@addition":380:"@2H10V@<2> Associative@D6H@axiom of@D6H@addition"& "@21H11V@("N(1)V$(1)O$N(3)V$(1)")"O$"6:H16:9999:H112:9999:X12:142X,52142X,148::L14:378:362:I04:366::O$"+":N(5)N(1)N(3):N(6)N(2)N(4)$"@22H5V@"N(1)V$(1)" "N(2)V$(2)" "N(3)V$(1)" "N(4)V$(2):I0:376:N(0)0O$"-":N(5)N(1)N(3)%O$(0)"ADD":O$(1)"SUBTRACT":"$"s. Arrange like terms in the@D2H@same column. Add each column."#Y84:H48:9999:"@R15C2H11V@To "S$" "P$"s, arrange@D2H@each in ascending powers of one of@D2H@their "V$"s. Arrange like terms@D2H@in each column. Subtract each@D2H@column.":930y$Y30C18V15H@"(N(6))"@18H@X@R15C@2@L138C22H@-@10C@"N(4)"@27H@Y@138C30H@+@10C@"N(7)"@35H@XY";:N(6)0ĺ"@L13H138C@-""n"@R15C0K@":930"P2210,1200A#Y36:H40:9999:"@R15C2H5V@To add "P$"s, arrange each in@D2H@ascending powers of one of their@D2H@"V2@L10C32H@"N(2)"@34H@XY@11H13V138C@-@R15C1H15V@SUBTRAHEND@UL10C4F@"N(3)"@18H@X@R15C@2@L138C22H@+@10C@"N(4)"@27H@Y@138C30H@-@10C@"N(5)"@34H@XY@138C15H16V@$$$$$$$$$$$$"!l382:N(6)N(1)N(3):N(7)N(2)N(5):"@L138C11H13V@+@14V@-@22H@-@30H@+":382p"m"@L1:X186:L35:10000:930; fI15:366::N(2)N(5)92150 h"@R15C1H5V@To "S$" "P$"s, add the@2D1H@additive inverse of each term in the@2D1H@subtrahend to like terms in the@2D1H@minuend.":382!j"@1H13V@MINUEND@UL138C22H@+@15H10C@"N(1)"@18H@X@R15C@$:922:1200C A"@22V1HI@..PRESS (SPACE BAR) TO CONTINUE...":250X C310:KY128323n E250:KY160323 H"@22V1H@"36)"@I@": ^VB%:HT%:MX%):PS%0:I0MX%:256I,32::16368,0:F2ĺ"@UL@" _HT%PS%F:"@I@"((256PS%))"@I@"; `31250:KY155CH%06 0CH%KY176:CH%MN%CH%MX%300< 2` 6GG(1):KY(16384):KY155ıw 8250:"@40X40YN@"; :KY(16384):KY128314 ;250:KY155Ĺ36309,0:26:DX$;"RUNALGEBRA 3" <KY205Mı =319 >:318 ?63900 @R624576:30719:63900` COPYRIGHT 1982 EDU-WARE SERVICES, INC. ALL RIGHTS RESERVED| F$"AM3.PROGRESS":10000:1002P::36312,C:X12:(36298X),NR(X)::36313,BG:36314,EN:16368,0:,310:KY128300 .   !!! ! ! ! ! !!!!!!!!!""" " " " " """""""""       ION","MULTIPLICATION","DIVISION","POLYNOMIAL TEST"D;(222)255Ħ;25:::"++ ERROR ++ "::" ERROR "(222)" AT LINE "(218)(219)256": AM3.2":3.2":PL1,YH:^: N26:(4)"OPEN"F$:(4)"READ"F$:I15:C(I)::C(1)5:W3C(1)1:C(2)3C(2)6x:*N(4)"CLOSE":35339::N26:(4)"UNLOCK"F$:(4)"OPEN"F$:(4)"WRITE"F$:NI15:C(I)::(4)"CLOSE":(4)"LOCK"F$:35339:2;PÃ"ADDITION AND SUBTRACT0)1VA$(0,0)""ıT9"@7V"92((M(0,1)))2(M(0,1)1VA$(0,1)"")"H@"M(0,0):q9M(0,1)1VA$(0,1)""ı9"@7V5H@"M(0,1):9M(1,1)1VA$(1,1)""ı9"@10V5H@"M(1,1):9'X9:L262 :'X,YHX,YXL,YXL,YHX1,YHX1,Y:XL1,YX1:EN%4:R1:2400:920:R2:3400:920:4000W8pIK6010:IK6020:IK6030:6040g8z6050:6060w86050:607086060:608086080:60708M(1,0)1VA$(1,0)""ı8"@10V"92((M(1,1)))2(M(1,1)1VA$(1,1)"")"H@"M(1,0):9M(0,C20H@"VA$(1,1)"@138C@+@10C30H@"VA$(0,1)"@138C@+@15C@"7P MX%2:VB%18:HT%4:350:HT%16:350:HT%26:350:MX%2:HT%35:350:I101:K101:PM(1,I)M(0,K):AA$AA$(P):K,I:8067R 321:L:C2İ922:12007 7200:26:(4)"RUNAM3.1.1"+8BG%0:390::VA$(0,0)"":VA$(0,1)VA$(1,1)34026L V(0)12:V(1)14:X01:"@L10C3H"V(X)"V@";:NPM(X,1):VP$VA$(X,1):416:"@138C@+@10C@";:NPM(X,0):VP$VA$(X,0):416:"@R15C@":57N 5:X12:21,131X77,131X::3:"@L10C8H17V@"VA$(0,1)VA$(1,1)"@138C@+@105VR15C@Multiply each of the terms in the@D2H@first "P$" by each in the@D2H@second. Then fill in the missing@D2H@"N$"al "C$"s in the@D2H@answer.@I@":X10:Y92:H64:L262:10000:LBG%EN%:378,6J Y12:H7:408:386:I01:368:388::VA$(1,0)"":K01:37$VA$(0,K):416:"@15C@)@138C@=@10C@";:NPP(I,K):VP$P$(I,K):416:"@I15C@":6000:"@I@":3824 PM$PM$"@L10C@"NP$:CO4PM$PM$"@138C@+"4 "@L1H18V@"PM$:380:"@10C@":6000:4:412:414:K,I:34G "@R15C@":321:L:922:12005H H48:406:"@2HX,0):VP$VA$(X,0):416:"@R15C@":3 I01:K01:COCO1:382:3:412:P(I,K)M(1,I)M(0,K):P$(I,K)VA$(1,I)VA$(0,K):VA$(1,I)VA$(0,K)P$(I,K)VA$(1,I)"@R15C@2@L10C@"]4 "@L15C2H15V@(@10C@";:NPM(1,I):VP$VA$(1,I):416:"@15C@)(@10C@";:NPM(0,K):VP4:410:378:386:CO0D2 I01:368:388::VA$(1,0)VA$(1,1)3301s2 K01:370:390::VA$(0,0)VA$(0,1)33022 I0:N(I)1:376:N(0)0VA$(R(2),0)"""3 V(0)7:V(1)10:X01:"@L10C5H"V(X)"V@";:NPM(X,1):VP$VA$(X,1):416:"@138C@+@10C@";:NPM(2:9999:"@2H12V@To multiply two "P$"s, use the@D2H@distributive axiom again. Multiply@D2H@each term of one "P$" by each@D2H@term of the other. Then add the@D2H@products.":9302 Y36:H80:9999:"@2H5V@MULTIPLY:@2D7F@MULTIPLICAND@4D18H@MULTIPLIER":L1otal area would be:@L10H17V@18Y@R@2@L@+15Y+2@R@":930;0= L0 P3210,12000 Y36:H48:9999:"@2H5V@To multiply a "P$" by a@D2H@"M$", use the distributive axiom@D2H@to multiply each term of the@D2H@"P$" by the "M$". Then add@D2H@the products."1 Y9:X13:"@10H"6X"V@<"X">"::"@10H11V@<4>@14H9V@THE DIFFERENCE OF TWO@D14H@SQUARES@D14H@"CH$(4)`"@10H13V@<0> RETURN TO ALGEBRA MENU@8DI11H@WHICH ONE (0-4) ??@I@"eMN%0:MX%4:300:CCH%:Cİ26:30976:DX$;"RUN ALGEBRA 3"jHD$CH$(C):910:92Y12X14,Y16X17,Y13XY:21,12214,11621,11042,11049,11642,12220,12213,11620,110:43,11050,11643,122:31,9831,11028,107:32,9832,11035,107:4:15:"<0>"Z59,3259,15960,15960,32b["@20H5V@CONTENTS":X12:"@14H"6X"V@"CH$(X)::R$"@R15C0K@"Z(36309)2BG1:EN4:R3:3400:36301,NR(3):920:26:DX$;"RUNAM3.4.1"L36309,0:C0:P0:M0:900:HD$"":910:X18:Y388616:H12:L27:10000:(Y10)8:"@3H@<"(Y22)16">"VY86ēX13,Y12X13,Y16:X10,Y13X13,Y16:X14,(HD$)76:H11:1000035339:R(I)((1)I):BG1:EN9:FG0:F2:I14:CH$(I)::PR(3,4),FA(3,4),PA$(2,4),PN(12):X112:PN(X)::DX$(4)I$"integer":F$"factor":N$"number":S$"prime":M$"monomial":P$"polynomial":W$"@R15C2H5V@":D$"@2D2H@"@"38)"@I@":q"@5H21VI@PRESS "(1)" TO VIEW THE NEXT PAGE.@3H22V@PRESS "(2)" TO VIEW THE PREVIOUS PAGE.@I@"310:KY128931250:KY136İ922:PP1:1220KY149İ920:PP1:1220931(36)2):X(36)73:Y(37)82:HD$" ";:LA$(1))(AA$(2))(TA$(2))802g."WRONG, OTHER FACTOR IS (";:MS0816:N(3)PV$(3)"+"N(4)PV$(4)")":0N(1)V$(1)V$(2)")":"@1H1V@C"C" P"P"@D1H@M"M:"@I2V7H@"31):24(HD$)2:HD$"@I@":31051:92430976 "@21V1HI@"38)"@D1H(R)NR(R)1:\$"WRONG, ANSWER IS":X192:382:"@L10C16V"H(X)2"H@"N(X10)"@R15C@"::&R$"@25H18V@";:(AA)(IN)802(L5C1ĺ"WRONG@L15C10H13V@=@138C2H16V@";:X1:418:R$:*"WRONG@L138C22H15V@"AA;R$:,R$"@2H18V@";:(AA$(1))(TN(I)22I23:366:N(I)2(N(I)2)444::wT1$"":T2$"":IY1(IA$):(IA$,IY,1)" "T1$T1$(IA$,IY,1):IY1(AA$):(AA$,IY,1)" "T2$T2$(AA$,IY,1):IA$T1$:AA$T2$: 700:"@R15C11H18V@";:IA$AA$804 ""RIGHT":NR(1)N(4)ePA(1)PA(2)PA(3)PA(4)PA(1)99PA(2)99PA(3)99PA(4)99PA(1)PA(4)PA(2)PA(3)436362:PV$(1)V$(1):PV$(2)V$(2):362:PV$(3)V$(1):PV$(4)V$(2):V$(1)PV$(1)V$(1)PV$(2)V$(2)PV$(1)V$(2)PV$(2)438362:I1:366:N(I)1$BX2:BY7:BW36:BH9(P5):360"@L15C9V"H"H@(@10C@"PP$"@138C@*@10C@"PP$"@15C@)@10C11V"H7(H7)7(H20)"H@"PP$"@R15C@2":R$:BX2:BY12:BH7:BW36:360X16:N(X)(PN(R(4)1))::PA(1)N(1)N(3):PA(2)N(2)N(4):PA(3)N(2)N(3):PA(4)N,88((A(X)14)Y)(28Z),96:Z,Y:(A(X)14),88(A(X)14),88:cPR(1,X);:PR(2,X)2ĺ"@R15C@2";:"@L15C@*@138C@"PR(1,X1);:PR(2,X1)2ĺ"@R15C@2";X2PO(1)1ĺ"@15C@*@138C@";PR(1,X);:PO(X)2ĺ"@R15C@2":PAPAPR(1,X)PO(X):X)PN(R(4)1):PR(2,X)R(2)1::PR(1,3)PR(1,1):X132:PR(1,1)PR(1,X1)410N(X)PR(1,1)PR(2,X)PR(1,X1)PR(2,X1)::N(1)N(3)N(1)9N(3)9410X14:PR(3,X)PR(1,X)PR(2,X)::=Y01:A(X)Y,80A(X)Y,88:Z01:((A(X)14)Y)(28Z)@<"P"> For all "I$"s I";:gBX2:BY13:BH6:BW17:360:BX21:BY13(L4)(C4):BH6(L4)(C4):360rAAT:X9:Y84:H72:L126:10000:X142:L130:10000BX2:BY7:BH10:BW16:360:BX19:BW19:360:W$"@18V@"35):PX14:FA(2,X)0:PR(1, ~AI0100:310::. 3:14,39265,39:a AA$"":IA$"":PM$"":NP$"":X14:PA(X)0:: 384:"@IR@":BX2:BY5:BHA:BW36:360:Y36:H(A1)8:9999 Y36:H104(16(P5)):9999Y36:H16:9999:H88:9999:R$"@12H5V@Rule of Factors@2H8V f351R gIN$"":I0PS%:IN$IN$((256I))::IN(IN$):"@R@":IA$IA$IN$:} hBIBYBYBH1:"@"BX"H"BI"V@"BW):: jX12:VR(6)84:V$(X)(V)::V$(1)V$(2)362 lV$(3)V$(1)V$(2): nN(I)R(9)1: zPL:900 |AI0150:310::0:KY128KY149352P a250:HT%PS%F:((256PS%));:KY155ESC%1:"@R@":d bKY141PS%359~ cKY136PS%PS%PS%1 dKY149PS%MX%PS%PS%1 eKYKY128:(KY47)(KY58)(KY45PS%0)ĖHT%PS%F:(KY);:256PS%,KY:PS%PS%1:PS%MX%359R(17)4:FA(1,4)X:XFA(1,2)2412:I17:XPN(I)2412E*n :T14*p XR(4)1:FA(2,X)12416:X1404:FA(2,X)1:FA(3,T)FA(1,X)::X12:"@R15C"13X"V21H@<"X"> "FA(3,X)"@29H@<"X2"> "FA(3,X2)::"@I21H17V@ WHICH (1-4)?@I@ @I@ "9+r MN%1:MX%4:@21H@SELECT A PRIME@D21H@FACTOR OF"[)b 406:BG1:EN4:LBGEN:402:R$"@31H12V@ ":378d)d 410)f "@L133C2H13V@"(N(1))"@R15C31H12V@"(N(1)):FA(1,1)PR(1,1):FA(1,2)PR(1,1)PR(1,2))j FA(1,3)PN(R(4)1):FA(1,3)PR(1,1)FA(1,3)PR(1,2)24108*l X(PA)R$"@19H@WHICH IS CALLED@D19H@THE GREATEST COMMON@D19H@FACTOR."R$[(_ 321:920::1200#)` A4:392:"@2H5V@Factor the large "N$" in the left@D2H@box. Then select from the right box@D2H@the "N$" that is a "S$" "F$" of@D2H@the large "N$".@I2H11V@FACTOR8C9V"H(X)1"H@";:418:;' X12:PR(1,X)PR(1,X2)2340h' PO(X)1:PR(2,X)PR(2,X2)PO(X)PR(2,X)' 382:R$"@12V2H@Common Factor@7F@Smallest Power":"@"12X"V8H@"PR(1,X)"@19F@"PO(X):382' "@L138C16V"03X"H@";:424E($ 382::"@L11H16V15C@="C@*@138C@"PR(1,X1):PR(2,X)2ĺ"@15C12V"H(X)4"H@*"R$& "@L133C15V"H(X)2"H@"(N(X))"@15C@=@138C@";:418:R$"@18V"H(X)2"H@ITS FACTORS ARE@D14B@"PR(1,X)","PR(1,X1)R$::321:920:"@L15C2H4V@SO:"' X132:R$"@7V"H(X)1"H@"(N(X))" FACTORED IS @L131)"@15C@"% PR(2,X)2ĺ"@L133C8V"(H(X)2)2(((PR(3,X))))"H@"(PR(3,X))"@15C@ * ";:416:"@L138C12V"H(X)2"H@"PR(1,X)"@15C@*@138C@"PR(1,X)6& PR(2,X1)2ĺ"@L133C8V"H(X)8"H@"(PR(3,X1))"@15C@":A(X)A(X)56:416:"@L138C12V"H(X)6"H@"PR(1,X1)"@15Y)141X,56(28Y)141X,64:(84Y)141X,56(84Y)141X,64:Y,X:X12:28,55X84,55X:169,55X225,55X:$ PA1:H(1)3:H(3)23:A(1)28:A(3)169:X132:PR(2,X)1ĺ"@L138C8V"H(X)"H@"PR(1,X)"@15C@ * "; % PR(2,X1)1ĺ"@L138C8V"H(X)8"H@"PR(1,Xth, but@D6H@use the smallest power."D$"<3> Multiply the least powers of the@D6H@common "S$" "N$"s together.":930# L14:378:410:X132:"@L133C4V"(10X1)2(((N(X))))"H@"(N(X))"@R15C@"::X01:Y01:(56Y)141X,48(56Y)141X,56o$ (289999:W$"To find the Greatest Common Factor@D2H@of two "I$"s:"D$"<1> Find the "S$" "F$"s of each@D6H@"I$". If the same "S$" is@D6H@used as a "F$" more than once,@D6H@express it as a power.";q#D$"<2> Take all of the "S$" "N$"s@D6H@that are a "F$" of boing"D$"them.":930-!P2210,2220,2230,1200!400:" and J,@2D9H@I@D4B@if - is an "I$", then J is a@D9H@J@2D4B@"F$" of I.":930!400:", J, and K,@2D6H@if I and J are "F$"s of K,@2D11H@K@7F@K@D6H@then -=J and -=I.@D11H@I@7F@J":930"Y36:H120:2H17V@2 * 2 * 3 * 5"R$:930 \W$"The biggest "I$" that is a "F$D$"of two other "I$"s is the"D$;:HD$"Greatest Common Factor":940!^". It can be"D$"found by taking the smallest powers"D$"used of the "S$"s that are "F$"s"D$"of both "I$"s, and multiply29H16V@7/6 = 1r1":930RW$"A "N$" can be "F$"ed until it@D2H@can be expressed as a product of@D2H@"S$" "F$"s.@D2H@Every "I$" can be written as a@D2H@unique combination of "S$" "N$"s.":382:"@L2H11V10C@60"R$ T382:"@L10C2H14V@4 * 15"R$:382:"@L10CS$" "N$:940:"."D$"Dividing it by all other"D$N$"s leaves a"D$"remainder.":382JX199:Y36:H16:L70:10000:H122:10000:"@33H5V@7":382:"@29H8V@7/2 = 3r1":382:"@29H10V@7/3 = 2r1":382:"@29H12V@7/4 = 1r3":382L"@29H14V@7/5 = 1r2":382:"@hat you multiplied are ";:HD$F$"s":940:"."D$;:HD$"Factoring a "N$:940@"means to find the"D$"set of "N$"s whose product is"D$"equal to that "N$".":930SHW$"A "N$" that has no"D$"positive "I$" "F$"s"D$"other than itself and one"D$"is a ";:HD$1:MCH%:920:36320M,(36320M)(36320M)255<P1200\900:C2000,3000,4000,5000b}M2100,2200,2310,24004P2110,2120,2130,2140,1200L>W$"When you multiply two "I$"s, you"D$"get their ";:HD$"product":940:". The two "I$"s"D$"t0nC34000&tC4P0:M0:1225P0:M0:900:"@12H5V@MODE SELECTION@2D4H@<1> DISCUSSION@2D4H@<2> RULE@2D4H@<3> EXAMPLE@2D4H@<4> SAMPLE PROBLEM@2D4H@<0> RETURN TO CONTENTS@6D5HI@WHICH ONE (0-4) ??@I@"MN%0:MX%4:300:CH%İ922:1100/P