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S S pp07 8`: @p9 8>30 @$ FfF@ #  0`@@@@`0? @@`0 a303a `08  0p`@q30p0031 Xp    16304,0:16297,0:16302,0:16299,0:768,0:769,0 PZ12500:Z:::10:16:"LOADING":12:5:"FACTORING ALGEBRAIC EXPRESSIONS":(13);(4);"RUN FACTORING",u 768,0:769,0K:10:16:"LOADING":12:11:"QUADRATIC EQUATIONS"s(13)(4)"RUN QUADRATIC EQUATIONS" AG E WILL BE A WORK AREA WHERE YOU WILL":"ENTER THE FACTORS."HmP50000:n7:"WHEN YOU START, EACH SET OF PARENTHESES ":"WILL CONTAIN AN "(34)"X."(34):13:"USING THE ARROW KEYS TO MOVE THE CURSOR,":"ENTER THE APPROPRIATE NUMBERS, SIGNS, OR":"LETT7:"DO YOU WISH TO REVIEW THE"::7:"INSTRUCTIONS (Y OR N)? ";:G$""htG$:G$"Y"G$"y"ĺG$:60000tG$"N"G$"n"60810:700t:ZZ769:N$""tI(ZZ):I060800:N$N$(I):ZZZZ1:60910PERENCE OF TWO SQUARES">l17:4:"4. COMMON FACTOR PROBLEMS"l 20:"YOU MAY CHOOSE ANY OF THESE TYPES OR YOU":"MAY MIX THEM."l50000::9l("FOR EACH PROBLEM, THE COMPUTER WILL":l2"DISPLAY THE POLYNOMIAL YOU WILL FACTOR.":;m<15:"THERW FOUR KINDS OF PROBLEMS: "`k4:4:"1. EASY QUADRATIC TRINOMIALS":6:7:"(COEFFICIENT OF ";kD(2)1:D(1)0:D(0)0:10000:" IS 1)":9:4:"2. HARD QUADRATIC TRINOMIALS"k11:7:"(COEFFICIENT OF ";:10000:" IS MORE THAN 1)"l14:4:"3. DIFFMPLETE THE PREMATURELY EXITED FOR LOOPS TO AVOID PROBLEMS WITH RETURN.Qj(59000fjx34,5::34,0:7xj:"RESULT":j10:6:25000j50000:34,5::34,0j7::"WORK SPACE":::4jCF%Ė11jj` PRINT INSTRUCTIONSjk"I KNO)POLY%(0)MU(0)58900*iRE%(0)058700Li$M1%(0)M1%(0):M2%(0)M2%(0)i.34,14::34,0:16:4:25000:50000:POLY%(2)MU(2)POLY%(1)MU(1)POLY%(0)MU(0)58900iLSC:FCi20:15::"THAT'S IT!"::50000FjSC12:SC:FC12:FC: MUST CO(2)POLY%(1)MU(1)POLY%(0)MU(0)58900@hM1%(1)M2%(1)58700jhM1%(0)FA%(0,SC,1):M2%(0)FA%(0,SC,0)hRE%(0)0M2%(0)M2%(0):58640hRE%(1)0M1%(0)M1%(0):M2%(0)M2%(0)i34,14::34,0:16:4:25000:50000:POLY%(2)MU(2)POLY%(1)MU(1M2%(0):585409gRE%(1)0M1%(0)M1%(0):M2%(0)M2%(0)g34,14::34,0:16:4:25000:50000:POLY%(2)MU(2)POLY%(1)MU(1)POLY%(0)MU(0)58900gRE%(0)058600gM1%(0)M1%(0):M2%(0)M2%(0)'h34,14::34,0:16:4:25000:50000:POLY%(2)MU,15::34,08f*"WE'LL TRY ALL POSSIBLE COMBINATIONS":cf4"OF THE ABOVE FACTORS UNTIL WE GET":vf>"A SOLUTION."fH50000fFC1N1%:M1%(1)FA%(1,FC,0):M2%(1)FA%(1,FC,1)fSC1N0%:M1%(0)FA%(0,SC,0):M2%(0)FA%(0,SC,1) gRE%(0)0M2%(0) BOTH BE":&eRE%(1)0ĺ"POSITIVE."AeRE%(1)0ĺ"NEGATIVE."Se50000:58400}e"SINCE THE LAST TERM IS NEGATIVE,":e"THE CONSTANTS IN THE FACTORS MUST":e"HAVE DIFFERENT SIGNS, ONE POSITIVE":e"AND ONE NEGATIVE."e50000 f 34(RE%(0)TF)1dfߢ8N0%:25:TF;6);(RE%(0)TF);9dp߂TFTd16:1:RE%(0)058100d"SINCE THE LAST TERM IS POSITIVE AND":d"THE LINEAR TERM IS ";:RE%(1)0ĺ"ALSO POSITIVE";:58040d"NEGATIVE"; e", THE"::"CONSTANTS IN THE FACTORS MUST%(2)TF)TFTFRE%(2)57160Pc N1%N1%1:FA%(1,N1%,0)TF:FA%(1,N1%,1)RE%(2)TFjc*ߢ8N1%:6:TF1ĺTF;c4ߺTF1);"X";5);:TFRE%(2)ĺRE%(2)TF;c>ߺ"X";cH߭RE%(0)TF(RE%(0)TF)TFTF(RE%(0))57200 dRN0%N0%1:FA%(0,N0%,0)TF:FA%(0,N0%,1)(0)R%(0)b۰50000:59000Mb޺"TO BEGIN, LIST THE FACTORS OF THE FIRST":|b޺"AND LAST TERMS, IGNORING THE SIGNS."::bް50000:34,5::34,0bޢ7:9:D(2)RE%(2):D(1)0:D(0)0:10000:29:(RE%(0))bN1%0:N0%0b ߁TF19c߭RE%(2)TF(REa.ۺ"X, AND":Ga8ۺ"THE SQUARE ROOT OF ";RE%(0);" IS ";R%(0);"."::saBۺ"THIS TELLS US THAT THE FACTORS ARE":aLۺ"(";:R%(1)1ĺR%(1);aVۺ"X+";R%(0);") AND (";:R%(1)1ĺR%(1);a`ۺ"X-";R%(0);")." bM1%(1)R%(1):M2%(1)R%(1):M1%(0)R%(0):M2%RE ROOTS OF THE":A`ں"FIRST AND LAST TERMS, THEN ONE FACTOR":p`ں"WILL BE THE SUM OF THE ROOTS, AND THE":`ۺ"OTHER FACTOR WILL BE THEIR DIFFERENCE.":50000`۹34,5::34,0:7`$D(0)0:"THE SQUARE ROOT OF ";:10000:" IS ";:R%(1)1ĺR%(1);-----";3_\ڹ34,5::34,0:7::"RESULT"::10:8:C_ڭD2%57000_ځZZ02:D(ZZ)RE%(ZZ):ZZ:"WE SEE THAT ";:10000:" IS THE DIFFERENCE":_ں"OF TWO SQUARES. THIS MEANS THAT WE":_ں"CAN USE A SPECIAL TECHNIQUE.":`ں:"IF WE TAKE THE SQUALY%(1):10000:")."^ٰ55800:D(2)0:D(1)POLY%(2):D(0)POLY%(1):"X(";:10000:") = ";:ZZ02:D(ZZ)POLY%(ZZ)::10000:59030_ٰ50000::"PROBLEM #"P:3::"FACTOR"::ZZ02:D(ZZ)POLY%(ZZ):ZZ:3:15:10000:::"-----------------------------------E IS NO CONSTANT WHICH IS A FACTOR":V]ٺ"OF BOTH TERMS. HOWEVER, BOTH TERMS ARE":]ٺ"DIVISIBLE BY X. TO FACTOR THIS ":]ٺ"EXPRESSION, WE SIMPLY FACTOR OUT AN X."::^فZZ02:D(ZZ)POLY%(ZZ):ZZ:10000:" = X(";:D(2)0:D(1)POLY%(2):D(0)PO:D(ZZ)POLY%(ZZ):ZZ:10000:" = ";F0%;"X(";:D(2)0:D(1)RE%(2):D(0)RE%(1):10000:")."\ٰ55800:D(2)0:D(1)RE%(2):D(0)RE%(1):F0%"X(";:10000:") = ";:ZZ02:D(ZZ)POLY%(ZZ):ZZ:10000:59030\ٺ"LOOKING AT THIS BINOMIAL, WE SEE THAT":%]ٺ"THER10000:") = ";:ZZ02:D(ZZ)POLY%(ZZ):ZZ:10000:59030_[غ"THERE IS ONLY ONE STEP LEFT.":[غ"EACH TERM IN THE POLYNOMIAL HAS":[غ"AN X IN IT. SO WE MUST ALSO":[غ"FACTOR OUT AN X. WHEN WE DO, WE GET":[غ"THIS RESULT:"::X\؁ZZ02------------------------")Z׭CF%560008Z׭FX%55500jZ׺"NOW THAT WE HAVE FACTORED OUT A ";F0%;",":Z׺"THE POLYNOMIAL CANNOT BE FURTHER":Z׺"SIMPLIFIED. THE POLYNOMIAL IS FULLY":Z׺"FACTORED.":558009[ׁZZ02:D(ZZ)RE%(ZZ)::F0%"(";: ";:ZZ02:D(ZZ)RE%(ZZ):ZZ:10000:" ).":[Yn״FX%55160:"NOW WE CONTINUE FACTORING."Yxװ50000::"PROBLEM #"P:3::"FACTOR"::3:10:ZZ02:D(ZZ)POLY%(ZZ):ZZ:10000ZׁZZ02:D(ZZ)RE%(ZZ):ZZ:" = ";F0%;"(";:10000:")"::"----------------):ZZ:F0%0F0%1M0%1:56000KXFׁZZ02:RE%(ZZ)RE%(ZZ)F0%:ZZ:M0%F0%~XP׺"FIRST, WE NOTICE THAT ";F0%;" IS A FACTOR":XZ׺"OF EACH TERM OF THE POLYNOMIAL."::"THEREFORE, WE CAN SIMPLIFY ";:ZZ02:D(ZZ)POLY%(ZZ):ZZ:10000:" AS":-Yd׺F0%;" (ֺ"I'M GOING TO SHOW YOU HOW TO FACTOR":KWֺ"THIS POLYNOMIAL.":50000:Wח:"PROBLEM #"P:3::"FACTOR"::ZZ02:D(ZZ)POLY%(ZZ):ZZ:3:15:10000:::"----------------------------------------"W ׭CF%FX%F0%255700X<ׁZZ02:RE%(ZZ)POLY%(ZZVPò SUBROUTINE: WAIT FOR6VZò USER TO HIT RETURN.nVnâ24:9:"PRESS ";::"RETURN";::" TO CONTINUE. ";|Vxù16368,0Ví(16384)1281350050Vù16368,0Vâ24:8:27);VñVֲ SHOW HOW TO FACTOR EXPRESSIONV֗:"OKAY, ";N$;".":*W6(G$))G$;:Uȯ769,0::9:T$"THANK YOU, "N$".":(40(T$))2)T$:" I HOPE YOU ENJOYED THIS PROGRAM.":" PRESS RETURN TO REBOOT THE DISK.":20:16368,0UүP$:P$(13)45010:(42204)238(42205)16(42206)192Č47731Uܯ(43626):40130T"S." Tœ50000:P0:VTG$(DD):3(G$))G$;:35:DD0G$"0.00":42020T G$(DDP):DDP(DDP)G$G$".00":42020T(G$,1)"."G$"0"G$T(G$,(G$)1,1)"."G$G$"0"T ZZ1(G$):(G$,ZZ,1)"."ĂT!G$(G$,ZZ2) U$TERM ..............";:DDTE%(6):40200:`S"LINEAR TERM ................";:DDTE%(7):40200:S"TOTAL ......................";:DDTE%:40200:SP0ĺ" YOU DID NOT COMPLETE ANY PROBLEMS.":40130T8)"YOU COMPLETED "P" PROBLEM";:P1ĺ".":TE%(1):40200:HRr"FINDING COMMON FACTORS .....";:DDTE%(2):40200:R|"DIFFERENCE OF TWO SQUARES ..";:DDTE%(3):40200:R"LEADING COEFFICIENT ........";:DDTE%(4):40200:R"SIGN OF CONSTANT TERM ......";:DDTE%(5):40200:(S"CONSTANT QA PRINTS ERROR SUMMARY5QB FOR ALL PROBLEMS.xQJPP1::11:"TOTAL ERROR ANALYSIS":34:"AVERAGE";:36:"PER"QT" ERROR";:27:"NUMBER PROBLEM";Q^" ----- ------ -------";Rh"INCORRECT FORMAT OF FACTORS ";:DDINEAR TERM ................. ";E%(7)hPE%0:T117:TE%(T1)TE%(T1)E%(T1):E%E%E%(T1):T1:TE%TE%E%nPP"TOTAL ....................... ";E%:P䉭E%2E%2PDD3E%(3(1)):1((40(ME$(DD)))2):ME$(DD)PH50000:Q@ TOTAL ERRORSACTORS . ";E%(1):@O"FINDING COMMON FACTORS ...... ";E%(2):nOꈺ"DIFFERENCE OF TWO SQUARES ... ";E%(3):O"LEADING COEFFICIENT ......... ";E%(4):O"SIGN OF CONSTANT TERM ....... ";E%(5):O"CONSTANT TERM ............... ";E%(6):$P"LN ERROR SUBROUTINE.7N PRINTS ERROR SUMMARYPN FOR THIS PROBLEM.gN UPDATES TOTALS.Nˆ:6:"ERROR SUMMARY FOR PROBLEM #"P::" ERROR NUMBER"N̈" ----- ------":Oֈ"INCORRECT FORMAT OF F MHb")";+Mpb"(";:M2%(1)1ĺ" ";:252208MzbM2%(1);BMb"X";]MbM2%(0)0ĺ"+";:25250gMb"-";Mb(M2%(0));:(M2%(0))10ĺ" ";Mb") = ";MbD(2)MU(2):D(1)MU(1):D(0)MU(0):10000M8cM0u DELAY SUBROUTINE -- 2 SEC.N:uDD11630:DD: SUBROUTINE,La DISPLAYS A MULTIPLICATIONLLa VARIABLES AS IN MULTIPLYWLa15000uLaM0%0M0%1ĺ" ";:25100LaM0%;L b"(";:M1%(1)1ĺ" ";:25120LbM1%(1);L b"X";L*bM1%(0)0ĺ"+";:25150L4b"-";M>b(M1%(0));:(M1%(0))10ĺ" ";%(0)10C2%(1)C2%(2)4K2ZLF%M1%(0):XF%LF%M1%(1)fK&RM1%(0)10C1%(1)C1%(2)Z>:RC2%(2)1M2%(0)C2%(1):21100~>DRC2%(1)1M2%(0)C2%(2):21100>NRM2%(0)10C2%(1)C2%(2)>lRM1%(1)0S1%0M2%(1)0S2%0(C1%(1)1C1%(2)1)(C2%(1)1C2%(2)1)OK%0:>vROK%1#?R5=PC2%(2)1:" ";(8);>=P21000: DIGEST NEW INFORMATIOND=Pn=R CHECK TO SEE THAT FACTORS ARE GOOD.= RHELP%T1%(36):T2%(37):T2%:36,START%15:10):T2%1:36,START%15:21);:36,T1%:37,T2%=RC1%(2)1M1%(0)C1%(1):21050>RC1%(699,20660,20699,20670,20680,20690,206992<}P20699JNM$" "İ206004CNM$(8)İ201004HNM$(21)İ202004MNM$"0"M$"9"İ20300Z5RNM$(13)(M0%M1%(1)1VE CURSOR."::10:"USE SPACEBAR TO ERASE."::17:"PRESS:"::" ";::"RETURN";::" WHEN DONE.";:22::"S";:3'N" TO SEE SOLUTION."::" ";::"H";::" FOR HELP.";:22::"Q";::" TO QUIT.";:V%1:START%13(NM$"H"M$"h"ĖSTART%3 4)NHELP%İU(1)M0%MU(1):MU(0)M0%MU(0)$2:<2 N ENTER SUBROUTINEZ2!N SET HELP% TO NON-ZEROv2"N TO DISPLAY RUNNING2#N PRODUCT.2%NV%(37):START%(36):HELP%0:14:1:"----------------------------------------";p3&N16:6:"USE ARROW KEYS TO MO: FACTORS IN,1: M1%(1-0), M2%(1-0)H1: PASS CONSTANT FACTOR`1: (IF ANY) IN M0%.z1: RESULT RETURNED IN1: MU(2-0).1:MU(2)M1%(1)M2%(1):MU(1)M1%(1)M2%(0)M1%(0)M2%(1):MU(0)M1%(0)M2%(0)2:M0%0M0%1MU(2)M0%MU(2):M0t'D(1)010200,0~'D(1)0D(2)0ĺ"+";C0'(D(1))1ĺD(1);V0'D(1)1ĺ"-";`0'"X";r0'D(0)0103000'D(0)0(D(2)0D(1)0)ĺ"+";0'D(0);0<(D(2)0D(1)0D(0)0ĺ0;0(0: MULTIPLY SUBROUTINE0: PASS COEFFICIENTS OF1:M1%(1)1:M1%(0)0'/FX%M0%150102/15000m/POLY%(2)MU(2):POLY%(1)MU(1):POLY%(0)MU(0):F0%M0%:/' DISPLAY SUBROUTINE/' PASS COEFFICIENTS OF POLY. IN/' D(2-0)/'D(2)010100/$'D(2)1ĺD(2);0.'"X";:(37):2;(10);.POLY%(2)MU(2):POLY%(1)MU(1):POLY%(0)MU(0):F0%M0%:`. CREATE A COMMON FACTOR PROBLEM..D2%0:CF%1:M0%R(9):FX%0:M1%(1)0:M1%(0)1:M2%(1)R(3):M2%(0)R(9):M2%(0)M2%(1)(M2%(0)M2%(1))5010.R(2)2M2%(0)M2%(0)/R(2)2FX%1DIVQQ(R%(0))4010+-M0%R%(1)294010d-(LC1%(M0%1R%(1)1))(LC1%M0%1R%(1)1)4010l-QQ-M1%(1)R%(1):M2%(1)R%(1):M1%(0)R%(0):M2%(0)R%(0)-QQ1P:R%(0)K1%(QQ)R%(1)K2%(QQ)4010-:K1%(P)R%(0):K2%(P)R%(1)-150009%(1)M1%(0)M2%(0))(M1%(1)1M2%(1)1M0%1)3010>, 15000y, POLY%(2)MU(2):POLY%(1)MU(1):POLY%(0)MU(0):F0%M0%:, CREATE A DIFFERENCE OF SQUARES PROBLEM.,LC1%LC1%-D2%1:CF%0:M0%1:R%(1)R(3):R%(0)R(9):QQ2R%(1):DIVQQ(R%(1))CREATE A HARD TRINOMIAL PROBLEM.|+ D2%0:CF%0:M0%1:M1%(1)R(3):M2%(1)R(3):M1%(0)R(9)SIGN(0):M2%(0)R(9)SIGN(0)+ M0%M1%(1)M2%(1)43010+ QQ29:DIVQQ(M1%(1))DIVQQ(M1%(0))DIVQQ(M2%(1))DIVQQ(M2%(0))3010+ QQ3, (M1%(1)M2INAL ERROR BREAKDOWN."*20:650K* CREATE AN EASY TRINOMIAL PROBLEM.*D2%0:CF%0:F0%0:M0%0:M1%(1)1:M2%(1)1:M1%(0)R(9)SIGN(0):M2%(0)R(9)SIGN(0):M1%(0)M2%(0)2010*15000*POLY%(2)MU(2):POLY%(1)MU(1):POLY%(0)MU(0): + )DM0%1ĺ"TIMES THE FACTOR OF ";M0%;" ";^)N"IS ";:D(2)0:D(1)POLY%(1):D(0)0:10000:"."o)X50000:1030)l16:(31(N$))2:"GOOD WORK, ";N$;".":)v13:"THAT IS CORRECT.")50000)35000: PRINT ERROR BREAKDOWN.)P*40000: FTHE LINEAR TERM LEFT."'(50000:10309(EF%(7)1900K(E%(7)E%(7)1u(12:"CLOSE, ";N$;", BUT NO CIGAR.":(&"TO GET THE LINEAR TERM TO MATCH, YOU":(0"MUST MAKE SURE THAT THE SUM OF THE":(:"PRODUCTS OF THE INNER AND OUTER TERMS":*".":4'"TO GET THE CORRECT CONSTANT TERM, THE":e'"PRODUCT OF THE CONSTANTS IN THE FACTORS":'M0%1ĺ"TIMES THE ";M0%;" YOU FACTORED OUT":'"MUST BE EQUAL TO ";POLY%(0);".";'EF%(7)1790(" FIX THIS TERM,"::"AND YOU JUST HAVE WRONG SIGN AS"::"WELL AS THE WRONG VALUE."::EF%(7)1670&"IF YOU FIX BOTH OF THESE ERRORS, THEN"::"GETTING THE LINEAR TERM WILL BE"::"THE LAST STEP."&50000:1030&EF%(6)1800&E%(6)E%(6)1'12:"YOU'RE NOT QUITE RIGHT, ";N$;MUST":J%m"HAVE DIFFERENT SIGNS: ONE POSITIVE"::"AND ONE NEGATIVE.";\%rEF%(7)1670%w" ONCE YOU CORRECT THE"::"SIGN, YOU CAN WORK ON THE LINEAR TERM.":1670=&|E%(6)E%(6)1:N$;", YOU HAVE MADE TWO MISTAKES."::"THE CONSTANT TERM HAS THE IS POSITIVE,"::"THE CONSTANT TERMS IN THE FACTORS MUST":$^"HAVE THE SAME SIGN: BOTH POSITIVE"::"OR BOTH NEGATIVE.";:1650$c12:"THAT ISN'T CORRECT, ";N$;".":%h"SINCE THE CONSTANT TERM IS NEGATIVE,"::"THE CONSTANT TERMS IN THE FACTORS EF%(7)1595Z#6"CORRECT THESE ERRORS BEFORE YOU TRY TO"::"GET THE RIGHT LINEAR TERM."k#;50000:1030}#@EF%(5)1700#EE%(5)E%(5)1#JEF%(6)1660#O(POLY%(0))11635#T12:"THAT ISN'T CORRECT, ";N$;".":<$Y"SINCE THE CONSTANT TERM%(6)E%(6)1:"IS INCORRECT.":1""EF%(7)1595;"'1590",E%(5)E%(5)1:E%(6)E%(6)1:"YOU HAVE MADE THREE ERRORS, ";N$;".": #1"THE ";:D(2)1:D(1)0:D(0)0:10000:" TERM IS WRONG, AND THE CONSTANT"::"TERM IS WRONG IN BOTH SIGN AND VALUE.":: FIX THE LINEAR TERM.";:15955!EF%(5)EF%(6)1580!"WELL, ";N$;", I SEE TWO PROBLEMS."::"FIRST, THE ";:D(2)1:D(1)0:D(0)0:10000:" TERM IS WRONG. SECOND,":!"THE CONSTANT TERM ";:EF%(5)E%(5)E%(5)1:"HAS THE WRONG SIGN."::1570"E0:D(0)0:10000:" TERM, THE PRODUCT OF THE":Y "COEFFICIENTS OF X IN THE FACTORS": M0%1ĺ"AND THE ";M0%;" WHICH YOU HAVE FACTORED OUT": "MUST BE EQUAL TO ";POLY%(2);"."; EF%(7)1595! " ONCE YOU GET THE"::"FIRST TERM, YOU CAN0:10000:" IS ";:D(2)0:D(1)R%(1):10000:", AND ":f"THE SQUARE ROOT OF ";T2%;" IS ";R%(0);"."w50000:1030EF%(4)1600E%(4)E%(4)1EF%(5)EF%(6)1550"YOU'RE A LITTLE OFF, ";N$;". TO GET":/ "THE RIGHT ";:D(2)1:D(1)PECIAL"::"METHOD FOR THIS KIND OF PROBLEM.":1499["YOU'RE CLOSE, BUT YOU HAVE THE":T1%POLY%(2):T2%POLY%(0):M0%0M0%1T1%T1%M0%:T2%T2%M0%6"WRONG FACTORS. LET ME GIVE YOU A HINT."::"THE SQUARE ROOT OF ";:D(2)T1%:D(1)0:D(0)к"THE RIGHT ANSWER."%_50000:10307xEF%(3)1500IE%(3)E%(3)1s"I'M AFRAID THAT'S WRONG, ";N$;".":MU(1)01460"IF YOU LOOK CAREFULLY, YOU'LL NOTICE"::"THAT THIS IS A DIFFERENCE OF TWO SQUARES"3"PROBLEM. YOU MUST USE A SHE PROBLEM.":1375UE%(3)E%(3)1:12:"I CAN SEE TWO MISTAKES, ";N$;"."::"YOU DIDN'T FACTOR OUT THE RIGHT COMMON"::"FACTOR, AND YOU DIDN'T USE THE PROPER"::"METHOD FOR A DIFFERENCE OF TWO SQUARES."Z:"IF YOU FIX THESE ERRORS, YOU'LL HAVE":: COMMON FACTOR.":13556A12:"NOT QUITE, ";N$;".":~F"THE TERMS OF THIS POLYNOMIAL DON'T"::"HAVE ANY COMMON FACTORS."KEF%(0)1ĺ:"FIND THE RIGHT FACTOR, AND YOU'RE DONE.":1375P:"GET THIS PART RIGHT, THEN WORRY"::"ABOUT THE REST OF T"."::M0%;" IS NOT THE LARGEST COMMON":n2"FACTOR OF ";POLY%(2);", ";POLY%(1);", AND ";POLY%(0);".":1355712:"SORRY, ";N$;"."::"YOU'VE LEFT OUT AN IMPORTANT STEP.":<"DON'T FORGET THAT ";POLY%(2);", ";POLY%(1);", AND ";POLY%(0)::"HAVE AHIS POLYNOMIAL ARE NOT"::"ALL DIVISIBLE BY ";`D(2)0:D(1)0:D(0)LF%:XF%D(1)D(0):D(0)0} 10000:".":50000:1030EF%(2)1400E%(2)E%(2)1EF%(3)1365#M0%0M0%11335(F0%0F0%11345)-12:"THAT'S NOT RIGHT, ";N$;THIS POLYNOMIAL.":50000:1030(F0%LF%(F0%LF%)XF%FX%)Ģ16:"YOU'RE ON THE RIGHT TRACK, ";N$;","::"BUT YOU DID NOT FIND THE LARGEST"::"COMMON FACTOR FOR THIS POLYNOMIAL.":50000:1030/16:"THAT'S NOT RIGHT, ";N$;"."::"THE TERMS OF TFX%XF%LF%F0%Ģ16:"VERY CLOSE, ";N$;"."::"YOU FOUND THE RIGHT COMMON FACTOR, BUT"::"YOU MADE AN ERROR IN COMPUTATION.":50000:1030LF%F0%FX%Ģ16:"YOU MADE A SMALL OVERSIGHT, ";N$;"."::"NOTICE THAT X IS ALSO A FACTOR IN EACH"::"TERM OF 0E%(2)E%(2)1LF%1XF%ĺ"YOU'RE NOT BEING CAREFUL, ";N$;"."::"DON'T FORGET THAT THE TERMS OF THIS"::"BINOMIAL HAVE A COMMON FACTOR."::"ONCE YOU REMOVE THAT FACTOR, YOU'LL BE":LF%1XF%ĺ"DONE WITH THIS PROBLEM.":50000:1030)0:QQ17:EF%(0)EF%(0)EF%(QQ):QQ7LEF%(1)1200IVE%(1)E%(1)1e`16:"SORRY, ";N$;".":j"ANY FACTOR MUST HAVE THE FORM AX+B,":t"WHERE A AND B ARE INTEGERS.":~50000:1030CF%1300EF%(0)EF%(2)0FX%XF%LF%F0%190;:1000012:1EF%(1)OK%:EF%(2)(F0%0M0%1F0%1M0%0F0%M0%):EF%(3)D2%(POLY%(2)MU(2)POLY%(1)MU(1)POLY%(0)MU(0)):EF%(4)POLY%(2)MU(2)$EF%(5)(POLY%(0))(MU(0)):EF%(6)(POLY%(0))(MU(0)):EF%(7)POLY%(1)MU(1)%)EF%(0----------------------------------------"?34,6:10::34,0Z 7::"WORK SPACE"::CF%Ė11:22000:HELP%OK%D(2)MU(2):D(1)MU(1):D(0)MU(0):20:" = ";:10000:1050CF%Ė4:20000:HELP%OK%D(2)MU(2):D(1)MU(1):D(0)MU(0):19:" = "%(QQ)0:QQ:TE%0( DO N% PROBLEMS.QP1N%:QQ17:E%(QQ)0:QQ:QUIT%0T%2000,3000,4000,5000:T%5ĴR(5)2000,3000,3000,4000,5000:"PROBLEM #"P:::"FACTOR":D(2)POLY%(2):D(1)POLY%(1):D(0)POLY%(0):3:15:10000)1:4:"$):QQ0765 N%0QQ5780-QQ67806G$;SQQ1QQ6QQ6N%0780dQQ6T%QQtQQ645000 :4:N$","::"YOU MAY TRY UP TO 9 PROBLEMS."::"HOW MANY WOULD YOU LIKE? ";:G$""*G$:N%(G$):N%08104G$;HQQ17:TE EASY QUADRATIC TRINOMIALS":F4:"2. HARD QUADRATIC TRINOMIALS":o4:"3. DIFFERENCE OF TWO SQUARES":4:"4. COMMON FACTOR":4:"5. MIXED PROBLEMS":N%0Ė4:"6. EXIT PROGRAM"20:8:"YOUR SELECTION: ";:G$""  G$:QQ(G:::13:"DO YOU WANT INSTRUCTIONS (Y OR N)? ";:G$""{G$:XX((78)(79))16:XX(XX):G$"Y"G$"y"ī60000:700G$"N"G$"n"670G$;:3:QQ19:K1%(QQ)0:K2%(QQ)0:"WHAT KIND OF PROBLEMS DO YOU WANT?":::4:"1.0lZH90G$(ZH32)7qN$N$G$:G$;:ZZZZ1:610EvZZ0610ax(8)" "(8);:ZZ1608{N$(N$,(N$)1):ZZZZ1:610:3:"HI, "N$"!"::"THIS PROGRAM WILL HELP YOU PRACTICE"::"FACTORING DIFFERENT KINDS OF ALGEBRAIC"::"EXPRESSIONS."E.o ]:3:" PLEASE ENTER YOUR FIRST NAME (UP TO"::" TEN LETTERS) AND PRESS .":::10)"NAME: "; `ZZ0:N$"":G$"":ZH0 bG$:G$(8)610:ZH(G$):ZH13ZZ0650 dZH8630 gZZ10610 iZH65ZH122610jZH90ZH9761;::2 7:6:"FACTORING ALGEBRAIC EXPRESSIONS"` 10:6:"BY MARK BERMAN AND KEVIN VESSIO" 12:11:"DESIGNED BY DON ROSS" 15:9:"MICROCOMPUTER WORKSHOPS"::15:"COURSEWARE" :16:"(C) 1984" &30000:30000 X GET STUDENT'S NAM6)"THESE PROBLEMS ARE NOT SO EASY."N ME$(7)"KEEP TRYING. YOU'LL GET IT." ME$(8)"DON'T BE DISCOURAGED. YOU'LL DO BETTER." (769)060900  PRINT A TITLE PAGE. ::ZZ140:1:ZZ:" ";:23:ZZ:" ";::ZZ122:ZZ:1:" ";:40:" "(0)"VERY IMPRESSIVE!"J nME$(1)"I SEE YOU'VE BEEN DOING YOUR HOMEWORK!"| xME$(2)"TOO BAD YOUR TEACHER CAN'T SEE THIS!" ME$(3)"WELL, WE CAN'T ALL BE PERFECT." ME$(4)"THAT WAS A GOOD TRY." ME$(5)"YOU ALMOST MADE IT ON THAT ONE."$ ME$(1%(1),M2%(1),ME$(8),MU(2),POLY%(2),R%(1),RE%(2)n FR(X)(X(1)1): RETURN RANDOM NUMBER BETWEEN 1 AND X PSIGN(X)(2R(2))3: RETURN RANDOM SIGN, 1 OR -1 ZDIVQQ(X)(XQQ)(XQQ): RETURNS 1 IF X IS A MULTIPLE OF QQ, 0 IF NOT. dME$l33,40:34,0" FACTORING4 VERSION 1.1P COPYRIGHT (C) 1983 BYn( MICROCOMPUTER WORKSHOPS2 PORTCHESTER, NY3 LAST UPDATE:11/21/844 BY: KEVIN VESSIO/ <K1%(9),K2%(9),C1%(2),C2%(2),D(2),E%(7),EF%(7),FA%(1,6,1),TE%(7),M                                              !":30000mUMMARY OF ALL YOUR ":"ERRORS."0l50000:l8:"IF YOU HAVE TO STOP BEFORE YOU FINISH ":"ALL THE PROBLEMS, PRESS THE ";::"Q";::" KEY TO"::"QUIT AND RETURN TO THE MAIN MENU."l&50000: m12:(40((N$)18))2:"HAPPY FACTORING, "N$"4::"H";::" FOR HELP TO KEEP TRACK OF FACTORS.":17:4::"S";mk|:" FOR SOLUTION TO PROBLEM.":50000:#l5:"AFTER EACH PROBLEM, I WILL GIVE YOU AN ":"ANALYSIS OF YOUR ERRORS.":12:"WHEN YOU FINISH A SET OF PROBLEMS, I ":"WILL GIVE YOU A SOU CAN'T DO A PROBLEM, PRESS THE ";::"S":::"KEY. I WILL THEN SHOW YOU HOW TO FACTOR ":"THE POLYNOMIAL."zjh50000:jr2:"ASKING FOR HELP DOES NOT COUNT AGAINST ":"YOU. DON'T BE AFRAID TO USE THESE ":"FEATURES.Akw10:"REMEMBER:":14:5:"IF YOU ARE WRONG, I WILL POINT OUT YOUR ":"MISTAKE AND GIVE YOU ANOTHER CHANCE."bi,50000:iT5:"IF YOU NEED HELP, PRESS THE ";::"H";::" KEY.":8:"I WILL HELP YOU BY KEEPING TRACK OF THE ":"PRODUCT AS YOU CHANGE THE FACTORS.mj^14:"IF YYOU MAKE A MISTAKE, MOVE THE CURSOR ":"OVER THE ERROR, ERASE IT WITH THE SPACE ":"BAR, AND ENTER THE CORRECTION."h50000:h5:"WHEN YOU FINISH FACTORING, PRESS THE "::"RETURN";::" KEY."Ui11:"IF YOU ARE RIGHT, I WILL TELL YOU SO.":17:9:N$",":10:8:"WOULD YOU LIKE TO TRY A"::8:"SAMPLE PROBLEM (Y OR N)? ";:16368,0s5G$:G$"N"G$"n"G$"Y"G$"y"60725:G$"N"G$"n"60800s:"Y";:16151,0:I1(N$):768I,((N$,I,1))::768I,0:(13)(4)"RUN SAMPLE"Ft:10:ES"+f17:4:"4. COMMON FACTOR PROBLEMS"pf 20:"YOU MAY CHOOSE ANY OF THESE TYPES OR YOU":"MAY MIX THEM."f50000::9f("FOR EACH PROBLEM, THE COMPUTER WILL":f2"DISPLAY THE POLYNOMIAL YOU WILL FACTOR.":(g<15:"THERE WILL BE A WORK ARBLEMS: "Me4:4:"1. EASY QUADRATIC TRINOMIALS":6:7:"(COEFFICIENT OF ";eD(2)1:D(1)0:D(0)0:10000:" IS 1)":9:4:"2. HARD QUADRATIC TRINOMIALS"e11:7:"(COEFFICIENT OF ";:10000:" IS MORE THAN 1)"f14:4:"3. DIFFERENCE OF TWO SQUAR"WORK SPACE":::4!dCF%Ė11'dAd` PRINT INSTRUCTIONSdj:7:"OKAY, "N$".":12:"THIS PROGRAM WILL HELP YOU PRACTICE":14:"FACTORING DIFFERENT KINDS OF ALGEBRAIC":16:"EXPRESSIONS."d16368,0:50000de"I KNOW FOUR KINDS OF PROSC:FC,c20:15::"THAT'S IT!"::50000cSC12:SC:FC12:FC: MUST COMPLETE THE PREMATURELY EXITED FOR LOOPS TO AVOID PROBLEMS WITH RETURN.c(59000cx34,5::34,0:7c:"RESULT":c10:6:25000c50000:34,5::34,0d7::2%(0)M2%(0)ib34,14::34,0:16:4:25000:50000:POLY%(2)MU(2)POLY%(1)MU(1)POLY%(0)MU(0)58900}bRE%(0)058700b$M1%(0)M1%(0):M2%(0)M2%(0)b.34,14::34,0:16:4:25000:50000:POLY%(2)MU(2)POLY%(1)MU(1)POLY%(0)MU(0)58900cLM1%(0)M1%(0):M2%(0)M2%(0)za34,14::34,0:16:4:25000:50000:POLY%(2)MU(2)POLY%(1)MU(1)POLY%(0)MU(0)58900aM1%(1)M2%(1)58700aM1%(0)FA%(0,SC,1):M2%(0)FA%(0,SC,0)aRE%(0)0M2%(0)M2%(0):58640 bRE%(1)0M1%(0)M1%(0):M(1,FC,1)<`SC1N0%:M1%(0)FA%(0,SC,0):M2%(0)FA%(0,SC,1)``RE%(0)0M2%(0)M2%(0):58540`RE%(1)0M1%(0)M1%(0):M2%(0)M2%(0)`34,14::34,0:16:4:25000:50000:POLY%(2)MU(2)POLY%(1)MU(1)POLY%(0)MU(0)58900`RE%(0)058600a"HAVE DIFFERENT SIGNS, ONE POSITIVE":@_"AND ONE NEGATIVE."K_50000^_ 34,15::34,0_*"WE'LL TRY ALL POSSIBLE COMBINATIONS":_4"OF THE ABOVE FACTORS UNTIL WE GET":_>"A SOLUTION."_H50000`FC1N1%:M1%(1)FA%(1,FC,0):M2%(1)FA%O POSITIVE";:58040$^"NEGATIVE";^^", THE"::"CONSTANTS IN THE FACTORS MUST BOTH BE":y^RE%(1)0ĺ"POSITIVE."^RE%(1)0ĺ"NEGATIVE."^50000:58400^"SINCE THE LAST TERM IS NEGATIVE,":^"THE CONSTANTS IN THE FACTORS MUST":'_TF(RE%(0)TF)TFTF(RE%(0))57200_]RN0%N0%1:FA%(0,N0%,0)TF:FA%(0,N0%,1)(RE%(0)TF)]fߢ8N0%:25:TF;6);(RE%(0)TF);]p߂TF]16:1:RE%(0)058100]"SINCE THE LAST TERM IS POSITIVE AND":^"THE MIDDLE TERM IS ";:RE%(1)0ĺ"ALS(1)0:D(0)0:10000:29:(RE%(0))2\N1%0:N0%0>\ ߁TF19n\߭RE%(2)TF(RE%(2)TF)TFTFRE%(2)57160\ N1%N1%1:FA%(1,N1%,0)TF:FA%(1,N1%,1)RE%(2)TF\*ߢ8N1%:6:TF1ĺTF;\4ߺTF1);"X";5);:TFRE%(2)ĺRE%(2)TF;\>ߺ"X";']H߭RE%(0)%(1)1ĺR%(1);$[`ۺ"X-";R%(0);")."][M1%(1)R%(1):M2%(1)R%(1):M1%(0)R%(0):M2%(0)R%(0)o[۰50000:59000[޺"TO BEGIN, LIST THE FACTORS OF THE FIRST":[޺"AND LAST TERMS, IGNORING THE SIGNS."::[ް50000:34,5::34,0"\ޢ7:9:D(2)RE%(2):D,5::34,0:7RZ$D(0)0:"THE SQUARE ROOT OF ";:10000:" IS ";:R%(1)1ĺR%(1);bZ.ۺ"X, AND":Z8ۺ"THE SQUARE ROOT OF ";RE%(0);" IS ";R%(0);"."::ZBۺ"THIS TELLS US THAT THE FACTORS ARE":ZLۺ"(";:R%(1)1ĺR%(1);[Vۺ"X+";R%(0);") AND (";:R MEANS THAT WE":7Yں"CAN USE A SPECIAL TECHNIQUE.":eYں:"IF WE TAKE THE SQUARE ROOTS OF THE":Yں"FIRST AND LAST TERMS, THEN ONE FACTOR":Yں"WILL BE THE SUM OF THE ROOTS, AND THE":Yۺ"OTHER FACTOR WILL BE THEIR DIFFERENCE.":50000 Z۹34WE SIMPLY FACTOR OUT AN X."::XفZZ02:D(ZZ)POLY%(ZZ):ZZ:10000:" = X(";:D(2)0:D(1)POLY%(2):D(0)POLY%(1):10000:")":59030XڭD2%57000XځZZ02:D(ZZ)RE%(ZZ):ZZ:"WE SEE THAT ";:10000:" IS THE DIFFERENCE":Yں"OF TWO SQUARES. THISROBLEM.":100V34,0::11:11:"ONE MOMENT, PLEASE.":20:(13)(4)"RUN FACTORING"I590300Vغ"NOW THERE IS ONLY ONE STEP LEFT.":ZVغ"EACH TERM IN THE POLYNOMIAL IS A":Vغ"MULTIPLE OF X. SO WE MUST ALSO":Vغ"FACTOR OUT AN X. WHEN WE DO, WE GET":Vغ"THIS RESULT:"::3W؁ZZ02:D(ZZ)POLY%(ZZ):ZZ:10000:" = ";F0%;"X(" ";F0%;"(";:10000:")"::"----------------------------------------"UU׭CF%56000dU׭FX%55500U׺"NOW THAT WE HAVE FACTORED OUT A ";F0%;",":U׺"THE POLYNOMIAL CANNOT BE FURTHER":U׺"SIMPLIFIED. THE POLYNOMIAL IS FULLY":V׺"FACTORED.":, WE CAN WRITE ";:ZZ02:D(ZZ)POLY%(ZZ):ZZ:10000:" AS":vTd׺F0%;" ( ";:ZZ02:D(ZZ)RE%(ZZ):ZZ:10000:" )":Tn׺"NOW WE CONTINUE FACTORING.":50000Txח::"FACTOR"::3:10:ZZ02:D(ZZ)POLY%(ZZ):ZZ:10000EUׁZZ02:D(ZZ)RE%(ZZ):ZZ:" =----------------------"0S ׭CF%FX%F0%255700lS<ׁZZ02:RE%(ZZ)POLY%(ZZ):ZZ:F0%0F0%1M0%1:56000SFׁZZ02:RE%(ZZ)RE%(ZZ)F0%:ZZ:M0%F0%SP׺"FIRST, WE NOTICE THAT ";F0%;" IS A FACTOR":=TZ׺"OF EACH TERM OF THE POLYNOMIAL."::"THEREFOREN$):768I,((N$,I,1))::768I,0:(13)(4)"RUN SAMPLE"r10:7:"DO YOU WISH TO REVIEW THE"::7:"INSTRUCTIONS (Y OR N)? ";:G$""rG$:G$"Y"G$"y"ĺG$:60000rG$"N"G$"n"60810:700YOU FINISH ":"ALL THE PROBLEMS, PRESS THE ";::"Q";::" KEY TO"::"QUIT."\q&50000:q010:N$", WOULD YOU LIKE TO TRY A SAMPLE PROBLEM (Y/N)? ";:16368,0q5G$:G$"N"G$"n"G$"Y"G$"y"60725:G$"N"G$"n"608009r:16151,0:I1(:" FOR SOLUTION TO PROBLEM.":50000:p5:"AFTER EACH PROBLEM, I WILL GIVE YOU A ":"SUMMARY OF YOUR ERRORS.":12:"WHEN YOU FINISH A SET OF PROBLEMS, I ":"WILL GIVE YOU A TOTAL ERROR ANALYSIS."p50000:Oq8:"IF YOU WISH TO STOP BEFORE YOU HOW TO FACTOR ":"THE POLYNOMIAL."4oh50000:or2:"ASKING FOR HELP DOES NOT COUNT AGAINST ":"YOU. DON'T BE AFRAID TO USE THESE ":"FEATURES.ow10:"REMEMBER:":14:4::"H";::" FOR HELP TO KEEP TRACK OF FACTORS.":17:4::"S";'p|NOTHER CHANCE."n,50000:nT5:"IF YOU NEED HELP, PRESS THE ";::"H";::" KEY.":8:"I WILL HELP YOU BY KEEPING TRACK OF THE ":"PRODUCT AS YOU CHANGE THE FACTORS.'o^14:"IF YOU CAN'T DO A PROBLEM, PRESS THE ";::"S":::"KEY. I WILL THEN SHOW THE SPACE ":"BAR, AND ENTER THE CORRECTION.";m50000:m5:"WHEN YOU FINISH FACTORING, PRESS THE "::"RETURN";::" KEY."n11:"IF YOU ARE RIGHT, I WILL TELL YOU SO.":15:"IF YOU ARE WRONG, I WILL POINT OUT YOUR ":"MISTAKE AND GIVE YOU AU START, EACH SET OF PARENTHESES ":"WILL CONTAIN AN X.":13:"USING THE ARROW KEYS TO MOVE THE CURSOR,":"ENTER THE APPROPRIATE NUMBERS, SIGNS, OR":"LETTERS."l50000:.m9:"IF YOU MAKE A MISTAKE, MOVE THE CURSOR ":"OVER THE ERROR, ERASE IT WITHNY OF THESE TYPES OR YOU":"MAY MIX THEM.":k50000::9gk("FOR EACH PROBLEM, THE COMPUTER WILL":k2"DISPLAY THE POLYNOMIAL YOU WILL FACTOR.":k<15:"THERE WILL BE A WORK AREA WHERE YOU WILL":"ENTER THE FACTORS."kP50000:l7:"WHEN YOT OF ";WjD(2)1:D(1)0:D(0)0:10000:" IS 1)":9:4:"2. HARD QUADRATIC TRINOMIALS"j11:7:"(COEFFICIENT OF ";:10000:" IS MORE THAN 1)"j14:4:"3. DIFFERENCE OF TWO SQUARES"j17:4:"4. COMMON FACTOR PROBLEMS"*k 20:"YOU MAY CHOOSE A,5::34,0:7i:"RESULT":1i10:6:25000Ji50000:34,5::34,0hi7::"WORK SPACE":::4uiCF%Ė11{ii` PRINT INSTRUCTIONSii"I KNOW FOUR KINDS OF PROBLEMS: "j4:4:"1. EASY QUADRATIC TRINOMIALS":6:7:"(COEFFICIEN:34,0:16:4:25000:50000:POLY%(2)MU(2)POLY%(1)MU(1)POLY%(0)MU(0)58900[hLSC:FCh20:15::"THAT'S IT!"::50000hSC12:SC:FC12:FC: MUST COMPLETE THE PREMATURELY EXITED FOR LOOPS TO AVOID PROBLEMS WITH RETURN.h(59000 ix342%(0)FA%(0,SC,0)5gRE%(0)0M2%(0)M2%(0):58640agRE%(1)0M1%(0)M1%(0):M2%(0)M2%(0)g34,14::34,0:16:4:25000:50000:POLY%(2)MU(2)POLY%(1)MU(1)POLY%(0)MU(0)58900gRE%(0)058700g$M1%(0)M1%(0):M2%(0)M2%(0)Oh.34,14:0:50000:POLY%(2)MU(2)POLY%(1)MU(1)POLY%(0)MU(0)58900PfRE%(0)058600rfM1%(0)M1%(0):M2%(0)M2%(0)f34,14::34,0:16:4:25000:50000:POLY%(2)MU(2)POLY%(1)MU(1)POLY%(0)MU(0)58900fM1%(1)M2%(1)58700gM1%(0)FA%(0,SC,1):M WE GET":e>"A SOLUTION."(eH50000\eFC1N1%:M1%(1)FA%(1,FC,0):M2%(1)FA%(1,FC,1)eSC1N0%:M1%(0)FA%(0,SC,0):M2%(0)FA%(0,SC,1)eRE%(0)0M2%(0)M2%(0):58540eRE%(1)0M1%(0)M1%(0):M2%(0)M2%(0)b4ߺTF1);"X";5);:TFRE%(2)ĺRE%(2)TF;Hb>ߺ"X";{bH߭RE%(0)TF(RE%(0)TF)TFTF(RE%(0))57200bRN0%N0%1:FA%(0,N0%,0)TF:FA%(0,N0%,1)(RE%(0)TF)bfߢ8N0%:25:TF;6);(RE%(0)TF);bp߂TFb16:1:RE%(0)058100(cAST TERMS, IGNORING THE SIGNS."::b(M1%(0));:(M1%(0))10ĺ" ";MHb")";Mpb"(";:M2%(1)1ĺ" ";:25220MzbM2%(1);Mb"X";MbM2%(0)0ĺ"+";:25250N%0:LFZOK%1%LPZM2%(0)M2%(0)S2%0LZZ15000>LdZHELP%ıLnZT1%(36):36,START%9:" = ";:D(2)MU(2):D(1)MU(1):D(0)MU(0):10000:36,T1%:La SHOW SUBROUTINELa DISPLAYS A MULTIPLICATIONLa VARIABLES AS IN MULTIPLYLa15000MaM0%%(1)C1%(2):23050KYM1%(0)0>KZC1%(1)1M1%(1)1:23050PKZM1%(1)C1%(1)tK ZC2%(2)1M2%(0)C2%(1):23090KZC2%(1)1M2%(0)C2%(2):23090KZM2%(0)10C2%(1)C2%(2)K2ZLF%M1%(0):XF%LF%M1%(1)L=PM2%(1)1:" X";:20695U=PS2%0:" ";:20695p=PC2%(1)1:" ";:20695=PC2%(2)1:" ";(8);=P21000: DIGEST NEW INFORMATION=P=R CHECK TO SEE THAT FACTORS ARE GOOD.A> RHELP%T1%(36):T2%(37):T22%1:20580NM$" "İ20600S3CNM$(8)İ20100h3HNM$(21)İ202003MNM$"0"M$"9"İ203003RNM$(13)(M0%M1%(1)1M2%(1)1S1%S2%C1%(1)1C1%(2)1C2%(1)1C2%(2)1)Ĺ34,13:23::34,0:V%1:4WN.":w2'N18::"H";::" FOR HELP."::18::"S";::" TO SEE SOLUTION."::18::"Q";::" TO QUIT.";:V%1:START%12(NM$"H"M$"h"ĖSTART%32)NHELP%İ21000:20020$3*N" ( X )( X )";:36,START%2:OK%0:M0%0:M1%(1)1:M2%(1)1:S1%0:S2%0:C1%OUTINE$1!N SET HELP% TO NON-ZERO@1"N TO DISPLAY RUNNINGR1#N PRODUCT.t1%NV%(37):START%(36):HELP%02&N14:1:"----------------------------------------":6:"USE ARROW KEYS TO MOVE CURSOR."::8:"PRESS: ";::"RETURN";::" WHEN DONESS CONSTANT FACTOR*0: (IF ANY) IN M0%.D0: RESULT RETURNED INW0: MU(2-0).0:MU(2)M1%(1)M2%(1):MU(1)M1%(1)M2%(0)M1%(0)M2%(1):MU(0)M1%(0)M2%(0)0:M0%0M0%1MU(2)M0%MU(2):MU(1)M0%MU(1):MU(0)M0%MU(0)0:1 N ENTER SUBR1))1ĺD(1); /'D(1)1ĺ"-";*/'"X";Z$SF$:2040:SF$Q1$H(SF$)5ĺ" TOO MANY CHARACTERS IN FACTOR":2590%RCH"):"ONE EQUAL TO ZERO AND SOLVE."FE1E11:2590:2030:620w2470:V5:H12:Z$"( )( ) = 0":20202030"ENTER FIRST FACTOR : ";:"";FF$:FF$""730Z$FF$:2040:FF$Q1$(FF$)5ĺ" TOO MANY CHARACTERS IN FACT7202030:PI2S712310[16:P1ĺ"THE COEFFICIENTS ";A;", ";B;", AND ";C:E1E11P1ĺ:"DO NOT HAVE A COMMON FACTOR.":2590:2030:620P3720"YOU MUST FACTOR FIRST. IF THE PRODUCT":"OF TWO FACTORS IS EQUAL TO 0, SET EAE$"X2 "" +X "C$" = 0":580I0B1E$"X2 "" -X "C$" = 0":580i:E$"X2 "B$"X "C$" = 0"DF1$"X"R1$:F3$"1X"R1$NF2$"X"R2$:F4$"1X"R2$X:" SOLVE":13:E$:E1$E$bV4:H0:Z$LI$:2020:2440l2030:2480vP2PI1(C):Z$C$:2000:C$Z$?B(R1R2):B$(B):Z$B$:2000:B$Z$NA1:A$"1"bB0B$"+ "B$vB0B$"- "B$C0C$"+ "C$C0C$"- "C$R10R1$"-"R1$R10R1$"+"R1$R20R2$"-"R2$R20R2$"+"R2$&B1 2) MORE DIFFICULT"J3290+TLD(G$)8^G91X8IhLD380,1760Rr330[|PI1{R1((1)181)9:R10390R1$(R1):Z$R1$:2000:R1$Z$R2((1)121)6:R20410R1R20390R2$(R2):Z$R2$:2000:R2$Z$CR1R2:C$(QQ128)G$"Y"4270+G$"N"220|:"YOU MAY TRY UP TO 9 PROBLEMS."::"HOW MANY WOULD YOU LIKE? ";:16368,0X8(16384):X8177X8185270X8X8176"16368,0,:"ENTER LEVEL OF DIFFICULTY:":6" 1) EASIER":@" ") BL$BL$BL$BL$BL$K :"HI! WHAT'S YOUR NAME ?";V "";N$e N$""160 (N$)10N$(N$,10) :"HI, ";N$;".": "DO YOU WANT INSTRUCTIONS (Y OR N)?" QQ(1):QQ(16384):QQ206QQ217220 16368,0:G$ UNDO MULTIPLICATION, YOU MUST"< ZM2$"THAT IS CORRECT."h dM3$"THE QUADRATIC EXPRESSION HAS BEEN" nM4$" IS POSITIVE, ITS FACTORS HAVE" xSI$(1)"+":SI$(2)"-" LI$"----------------------------------------" BL$" 1 QE124::" ":QE6 24:QE140::" ";:QEV QE122:40:QE::" ":QE\  10:7:"SOLVING QUADRATIC EQUATIONS" (:15:"BY DON ROSS" 2:9:"MICROCOMPUTER WORKSHOPS" <:16:"(C) 1983" FX12500:X G34,0 PM1$"TOCM$(8)"THESE PROBLEMS ARE NOT SO EASY."R CM$(9)"KEEP TRYING. YOU'LL GET IT."  Line 20 patches monitor COUT routine. (Usually at $FDF0) CM$(10)"DON'T GET DISCOURAGED. YOU'LL DO BETTER NEXT TIME." : 1 QE140:" ";:QE:34,SEE YOU'VE BEEN DOING YOUR HOMEWORK."W CM$(3)"TOO BAD YOUR TEACHER CAN'T SEE THIS." CM$(4)"MAY THE FORCE BE WITH YOU !" CM$(5)"WELL, WE CAN'T ALL BE PERFECT." CM$(6)"THAT WAS A GOOD TRY." CM$(7)"YOU ALMOST MADE IT ON THAT ONE."( lC I768817:QQ:I,QQ:I:768:169,12,133,54,169,3,133,55,32,234,3,96,201,137,240,24,201,142,240,25,201,135,240,13,201,141,208,6,169,255,133,50,169,141,76,240,253,76,26,252,169,63,133,50,96,169,255,76,42,3 CM$(1)"VERY IMPRESSIVE !"% CM$(2)"I                        IT IS BETTER TO SIMPLIFY THE EQUATION":E1E11:d& P1ĺ"BY FACTORING OUT THE GREATEST COMMON":& P1ĺ"FACTOR OF THE COEFFICIENTS.":2590:620&$ "ENTER NUMBER TO BE DIVIDED INTO EACH "::"TERM";&. ": ";G$'8 (G$)0ĺ"";(BL$,80);")"-"M2M2 %F$(1)"X"M11;%F$(2)"X"M1(F$(1))l%S30:X1L:(F$(X))48(F$(X))57S3S31s%X%S32S21%%S70:A2(A2)B2(B2)C2(C2)S71:CF2%A3(A3)B3(B3)C3(C3)S71:CF3%0& P1ĺ"L3S21:!$4X1L:F$(X)"":X?$>X1L:F$(X)(Z$,X,1):XH$HPS0u$RX2L1:F$(X)"+"F$(X)"-"PSX:XL1|$\X$fPS0S21:$pF$(PS1)"X"S21:$zXPS1L$(F$(X))48(F$(X))57S21:$X$M2((Z$,PS1)) %F$(PS#2280:600;#H0:V5:Z$"":34,5:10::34,0:2020:W#(Z$,1)"-"Z$(Z$,2)]#q#V1:H1:Z$:#34,15:18::34,0:#Q1$""#X1(Z$)# Z5$(Z$,X,1):Z5$"("Z5$")"Z5$" "Q1$Q1$Z5$#X# Z$Q1$: $*L(Z$):B0B$(B)""XB0B$"+"(B)2"bCF(2)F(4)C"lC0C$(C)X"vC0C$"+"(C)h"B1B$"+"y"B1B$"-""A1A$"""E$A$"X2 "B$"X "C$" = 0""F1$F$(1)"X"F$(2):F2$"X"F$(4):F4$"1"F2$#PI1F3$"1"F1$:F4$"1"F2$((1)121)6:F(4)01780;!F$(1)(F(1)):F$(3)(F(3))P!F(1)1F$(1)""j!F(2)0F$(2)(F(2))!F(2)0F$(2)"+"(F(2))!&F(4)0F$(4)(F(4))!0F(4)0F$(4)"+"(F(4))!:AF(1)F(3):A$(A)!DBF(1)F(4)F(2)F(3):B01760 "N ----- -----------"U "COMPUTATIONAL "E(2)" "((E(2)G9)100)100 "PROCEDURAL "E(1)" "((E(1)G9)100)100 ::"HOPE YOU HAD FUN!!":0: PI2:F(1)((1)22):F(3)1 F(2)((1)81)4:F(2)01770!F(4)5E1E24H110:H286R3((1)(H1H21)H2)G:CM$(R3):oE(1)E(1)E1:E(2)E(2)E2:E10:E20y2590G9G9G91:"ERROR ANALYSIS":G$"*"G9G91G90G91" TOTAL PER PROBLEM" " :HH(2):Z$" "SO$(2):20204T2030:N$;", ";M2$:j^"THESE ARE THE SOLUTIONS TO THE EQUATION.":2590h2030:"ERROR ANALYSIS:":r" PROCEDURAL ERRORS : ";E1:|" COMPUTATIONAL ERRORS : ";E2}E1E21H14:H21~E1E21H17:H2030:2640.PI1ĭP3P4İ2810:2590:1500>2030:2830SS61S60:1500bPI11590tZ(W1)11590S51:2030:2640"2030:2830,S61S60:15606V7:H25:Z$SF$" = 0":2020@VV(1):HH(1):Z$" "SO$(1):2020JVV(2)0&xPI1ĭP3P4İ2810:2590:139062030:2830KS61S60:1390ZPI11480pPI2Z(1)114802030:26402030:2830S61S60:1450V7:H7:Z$FF$" = 0":2020S50:S60:S42:V7:H25:Z$" "SF$" = 0":2020 2" = 0":2020J2Z$FF$:2090:Z(1)M1:Z(2)M2:Z$SF$:2090:Z(3)M1:Z(4)M2p<Z$(1)((Z(1))):Z$(3)((Z(3)))FZ(2)0Z$(2)"+"((Z(2)),2)PZ(2)0Z$(2)(Z(2))ZZ(4)0Z$(4)"+"((Z(4)),2)dZ(4)0Z$(4)(Z(4))nS50:2030:26414:H0:Z$"":20203P1ĺ"AFTER ";M3$:E1E11:sP1ĺ"FACTORED EACH FACTOR MUST THEN BE SET"::"TO ZERO."P11300P2ĺM3$::"FACTORED.":E1E11 P313102590:1240V7:H0:Z$(BL$,39):2020 (S41:V7:H7:Z$" "FF$6:H0:Z$"":2020B"ALL FACTORS MUST BE IN THE FORM OF AX+B":s"OR X+B, WHERE A AND B ARE INTEGERS.":2590S20:S12720S10:2030:N$;","::"I'M GOING TO SHOW YOU HOW TO":"FACTOR THIS EXPRESSION.":2590:36402480:2030:VWE$A1$"X2 "A2$"X"?V(A2$)1WE$A1$"X2 ""+X"A3$a`(A2$)0WE$A1$"X2 "A3$j(A2$)1WE$A1$"X2 ""-X"A3$tV16:H0:Z$"":2020~"(";FF$;")(";SF$;") = ";WE$S11ĺ:"TRY AGAIN.":2590:7202590:1210V117Z$FF$:2090:Z1M1:Z2M2:Z$SF$:2090:Z3M1:Z4M2FS211180gA1$(Z1Z3):Z1Z31A1$""$MTZ1Z4Z2Z3:A2$(MT):MT0A2$"+"A2$.A3$(Z2Z4):Z2Z40A3$"+"A3$8(A3$)0A3$""BWE$A1$"X2 "A2$"X "A3$L(A3$)0:J$(2)"X"96`Y0:C1(C):X1(C1):C1X(C1X)3710J6jYY1:K(Y)Xs6tK$(Y)(X):K1(Y)C1X:K1$(Y)(C1X)6~X:NFY619906H0:V4:Z$"":20206"LIST ALL FACTORS OF THE FIRST AND LAST":6"TERMS WITHOUT REGARD TO SIGN."72590*5 QU$Z$(W2)"/"Z$(W1):QUZ(W2)Z(W1)J5V12:HW52:Z$"X = "QU$Z5QU0HH1l5H(S4)H:20205$PI2SO$(S4)Z$:V(S4)125.58S80:20305BI$" ":PI1J$(1)"X":J$(2)"X"5LPI2A2J$(1)"2X":J$(2)"X" 6VPI2A3J$(1)"3X"3 4 2020.4 V9:HW5:Z$"---------":2020J4 (Z$(W1))1Z$(W1)" "~4 Q21ĭ(Z$(W2),1,1)"+"Z$(W2)" "(Z$(W2),2)4 V10:HW5:H(S4)H:Z$Z$(W1)"X ="Z$(W2)4 PI2Z(W1)1HW514 2020:PI1(PI2Z(W1)1)SO$(S4)Z$:V(S4)105 "2 "MT$"X"C$(3f M50E2$J$(1)C$F3p H12:V14NF:Z$E2$:2020R3z 2590:~3 H12:V14NF:Z$" "(E$,(E$)3):20203 T11:H9:V16NF:Z$" THAT IS CORRECT.":2020:2590:3 3330:S514 V8:HW52:Z$Z$(W2)" "Z$(W2):PI2Z(W1)1HW5111200:X1:%2 I$"":S91I$" "+2 X2 T10:F5$J$(1)S1$K1$:F6$J$(2)S2$K2$2* F5$F1$F6$F2$F5$F2$F6$F1$346024 U1(S1$K1$):U2(S2$K2$):M5AU2U12> MT$(M5):M50MT$"+"MT$2H M51MT$"+"2R M51MT$"-"3\ E2$J$(1)G$Z$(W1)33101 3330T1 V11:HW51:Z$Z$(W1)"X/"G$" ="Z$(W2)"/"G$:2020^1 3580d1 1 16384,128:G$((16384)128):16368,01 1 2030:M1$:E2E21:1 "DIVIDE BY THE COEFFICIENT OF X: ";Z(W1):2590:2030:32102 :M2$:X:M1$::0l "MULTIPLY BY THE RECIPROCAL OF THE":E2E21:k0v "COEFFICIENT OF X: ";G1$:2590:2030:30700 S50İ2810:2590:S61:0 "DIVIDE EACH SIDE BY THE SAME NUMBER":0 "";G$:(G$)0ĺ"";(BL$,80);"";:32200 Z$G$:2040:G$Z$1 :(G$)0ĺ"";(BL$,80);"";:3080:/ Z$G$:2040:G$Z$Z/ Z(W1)2G1$"1/2":G2$".5"y/& Z(W1)3G1$"1/3"::G2$""/0 G$G1$G$G2$3170/: 3330/D V11:HW55:Z$"("Z$(W1)"X)("G$")=""("Z$(W2)")("G$")":2020/N 3580/X 0b 2030"";:2990!. (G$)Z(W2)3030+. 34801. O. 2030:"SORRY, ";N$;".":. "UNDO ADDITION BY SUBTRACTING ";Z(W2)::"FROM BOTH SIDES.". 2590:E2E21:2980. S50İ2810:2590:S61:. "MULTIPLY EACH SIDE BY THE SAME NUMBER":$/ "";G$W2)2940-h 3480-r 6-| 2030:"SORRY, ";N$;".":z- "UNDO THE ADDITION BY ADDING ";(1)Z(W2)::"TO BOTH SIDES."- 2590:E2E21:2890- S51İ2760:2590:- "ENTER VALUE TO BE SUBTRACTED-EACH SIDE:": . "";G$:(G$)0ĺ"";(BL$,80);ST.":E1E11:%, SOLVE EACH FACTOR>, S41W11:W22:W56X," S42W13:W24:W524b,, 2030},6 P2880,2970,3060,3200,@ S51İ2760:2590:,J "ENTER VALUE TO BE ADDED TO EACH SIDE:":,T "";G$:(G$)0ĺ"";(BL$,80);"";:2990-^ (G$)Z()422710+ (G$)421700<+ Q20:P(G$):P1P2Q21B+ L+ 2030Y+ S51ı+ "TO SOLVE FOR X, YOU MUST UNDO ";Z(W1):+ "BY MULTIPLICATION OR DIVISION":E1E11:S61:+ Z(1)1HW51+ 2030, "UNDO ADDITION OR SUBTRACTION FIR THE FOLLOWING: (* TO QUIT)""*d L*n "1) ADD SAME NUMBER TO BOTH SIDES":}*x "2) SUBTRACT SAME NUMBER FROM BOTH SIDES":* "3) MULTIPLY BOTH SIDES BY SAME NUMBER":* "4) DIVIDE BOTH SIDES BY SAME NUMBER";* 3290 + ((G$)49(G$)52)(G$EACH FACTOR = 0 AND SOLVE";%) 3290M) ((G$)49(G$)51)(G$)422540`) (G$)421700l) P(G$)r) ) X11300:X1)( 24:7:"HIT RETURN TO CONTINUE.";)2 16368,0:3290)< (G$)132610)F 2030:)P 2030:16*Z "ENTER ONE OF0$( V5:H0:Z$" WORK AREA":2020.( 24704( P( V14:H0:Z$LI$:2020:i( V14:H0:Z$"":2020( "ENTER ONE OF THE FOLLOWING: (* TO QUIT)"( ( " 1) DIVIDE BOTH SIDES BY A NUMBER":( " 2) FACTOR THE LEFT SIDE":) " 3) SET ";:2340'B (G$)CF2420G'L 2030:"SORRY, ";N$;","::(G$)12400'V (G$);" IS NOT A FACTOR OF ";A;", ";B;" AND ";C;".":'` "THE GREATEST COMMON FACTOR IS ";CF;".":E2E21'j 2590:2030:2310't F(1)F(1)CF:F(2)F(2)CF:PI1:S01(~ 179"DIVIDING BOTH SIDES BY A NUMBER WILL"-Fq[Fz"ONLY COMPLICATE THINGS. WE DO NOT YET"aF{F"HAVE FACTORS TO SET = 0. THUS WE MUST"FF"FACTOR THE LEFT SIDE -- OPTION 2."F2590:F:"WORK AREA";::" ( )( ) = 0")G"--------------------------------"FE:"THESE WILL BE YOUR OPTIONS:":uE>"ENTER ONE OF THE FOLLOWING: (* TO QUIT)"{E?ER" 1) DIVIDE BOTH SIDES BY A NUMBER"E\" 2) FACTOR THE LEFT SIDE"Ef" 3) SET EACH FACTOR = 0 AND SOLVE"Eg'Fp: IN COMPUTATION ARE GIVEN. YOU":QD"THEN HAVE THE OPTION TO CONTINUE OR TO":jD"EXIT THE PROGRAM."vD2590:D "LET'S RUN THROUGH A SAMPLE PROBLEM."D2590:D :"SOLVE";::" 2"D*" X - 4X - 12 = 0"!E9"--------RED.":8C"EACH EQUATION CONTAINING THE FACTORS IS":eC"THEN SOLVED ON THE SCREEN USING THE":C"RULES FOR SOLVING LINEAR EQUATIONS.":C"AFTER BOTH SOLUTIONS HAVE BEEN FOUND,":C"THE NUMBER OF ERRORS INVOLVING USE OF A":!D"RULE OR ENTER THE":5Bv"FACTORS ON THE SECOND TRY, THE":dB"PROGRAM WILL BRANCH TO A SECTION THAT":B"WILL SHOW YOU HOW TO FACTOR THE":B"EXPRESSION.":2590:B"AFTER THE EXPRESSION HAS BEEN CORRECTLY":C"FACTORED, OPTION #3 MUST BE ENTEOTHERWISE OPTION #2 MUST BE CHOSEN.":2590:ZAD"YOU WILL BE ASKED TO ENTER THE FIRST":AN"AND SECOND FACTOR IN ANY ORDER. IF THE":AX"FACTORS ARE INCORRECT, THE":Ab"PRODUCT AND AN ERROR MESSAGE WILL BE": Bl"PRINTED. IF YOU ARE UNABLE TO BY THE SAME VALUE":C@" 2) FACTOR THE QUADRATIC EXPRESSION":s@" 3) SET EACH FACTOR TO ZERO AND SOLVE":@"IF THE COEFFICIENTS OF ALL TERMS HAVE A":@&"COMMON FACTOR GREATER THAN 1, THEN":@0"OPTION #1 MUST BE CHOSEN FIRST.":,A:"Y:":O?" 1) EASIER - THE COEFFICIENT OF THE"::" QUADRATIC TERM IS 1."?:" 2) MORE DIFFICULT - THE COEFFICIENT"::" OF THE QUADRATIC TERM IS 2 OR 3."?2590?:"YOU WILL BE GIVEN A MENU WITH 3 OPTIONS:"@" 1) DIVIDE EACH TERM020:3360>T11İ1990:720%>XX>:"ALL QUADRATIC EQUATIONS IN THIS PROGRAM":>"ARE GENERATED RANDOMLY IN THE FORM":>5:3:"2">"AX +BX+C=0 AND ARE SOLVABLE BY>:"FACTORING. YOU MAY CHOOSE FROM TWO":?"LEVELS OF DIFFICULT0:720D=TS9L2:3340:V10NF:H12L3:Z$K1$(X)I$:K1$K1$(X):2020x=^S9L1:3340:H19(J$(2)):Z$K$(X)I$:K2$K$(X)=h2020:3360=rT11İ1990:720=|S80PI14260=H11L3:V10NF:S1$SI$(I1):Z$S1$:2020 >H18L4:S2$SI$(I2):Z$S2$:21$K$(X)><S9L2:3340:H19L4:Z$K1$(X)I$:K2$K1$(X):2020H<3360]<T11İ1990:720q<PI2S804180<"PI1S804260<,PI1S814180<6H11L3:V10NF:S1$SI$(I2):Z$S1$:2020<@H18L4:S2$SI$(I1):Z$S2$:2020:3360=JT11İ199"TRY ALL COMBINATIONS OF THE ABOVE":U;"FACTORS. YOU WILL EITHER GET THE CORRECT";"PRODUCT OR RUN OUT OF POSSIBILITIES.";2590;X1NF;L1(K$(X)):L2(K1$(X)):L3(J$(1)):L4(J$(2))<S9L1:3340:V10NF:H12L3:Z$K$(X)I$:2020:KTORS MUST"::S81;:n"HAVE OPPOSITE SIGNS: 1 NEGATIVE,":X:x"1 POSITIVE.":I11:I22:H11:V10NF:Z$J$(1):2020:H18:Z$J$(2):2020:S1$SI$(I1):S2$SI$(I2):H11(J$(1)):V10NF:Z$S1$:2020:H18(J$(2)):Z$S2$:2020:2590:%;ALSO POSITIVE":B10ĺU9<"THE FACTORS OF ";C;" ARE BOTH POSITIVE.":I11:I21:3970k9F"SINCE ";C;M4$:9P"THE SAME SIGN. SINCE ";B;" IS NEGATIVE":9Z"THE FACTORS OF ";C;" ARE BOTH NEGATIVE.":I12:I22:3970:d"SINCE ";C;" IS NEGATIVE ITS FAC=8"OF THE ABOVE FACTORS AND SEE IF ANY OF"::"THEM WORK."m82590:H10:V10NF:Z$"( )( )":20208 H11:V10NF:Z$J$(1):2020:H18:Z$J$(2):202082030::C039408B039108("SINCE ";C;M4$:92"THE SAME SIGN. SINCE ";B;" IS :1990B7H5:V6:Z$" "A$"X2  "(C1):2020i7V8:H3:Z$J$(1)" "J$(2):20207H22:V88(NF1):Z$" "(K(V7))" "(K1(V7))72020:V72030:H0:V16:Z$"":20207"NOW,WE'LL TRY ALL POSSIBLE COMBINATIONS":L.":50000:1030(F0%LF%(F0%LF%)XF%FX%)Ģ16:"YOU'RE ON THE RIGHT TRACK, ";N$;","::"BUT YOU DID NOT FIND THE LARGEST"::"COMMON FACTOR FOR THIS POLYNOMIAL.":50000:1030!16:"THAT'S NOT RIGHT, ";N$;"."::"THE TERMS OF THIS POLYNOMIAL0%Ģ16:"VERY CLOSE, ";N$;"."::"YOU FOUND THE RIGHT COMMON FACTOR, BUT"::"YOU MADE AN ERROR IN COMPUTATION.":50000:1030LF%F0%FX%Ģ16:"YOU MADE A SMALL OVERSIGHT, ";N$;"."::"NOTICE THAT X IS ALSO A FACTOR IN EACH"::"TERM OF THIS POLYNOMIA900E%(2)E%(2)1LF%1XF%ĺ"YOU'RE NOT BEING CAREFUL, ";N$;"."::"DON'T FORGET THAT THE TERMS OF THIS"::"BINOMIAL HAVE A COMMON FACTOR."::"ONCE YOU REMOVE THAT FACTOR, YOU'LL BE"::"DONE WITH THIS PROBLEM.":50000:1030}FX%XF%LF%F(0)0:QQ17:EF%(0)EF%(0)EF%(QQ):QQ9LEF%(1)1200KVE%(1)E%(1)1g`16:"SORRY, ";N$;".":j"ANY FACTOR MUST HAVE THE FORM AX+B,":t"WHERE A AND B ARE INTEGERS.":~50000:1030CF%1300EF%(0)EF%(2)0FX%XF%LF%F0%1 ";:1000012:1EF%(1)OK%:EF%(2)(F0%0M0%1F0%1M0%0F0%M0%):EF%(3)D2%(POLY%(2)MU(2)POLY%(1)MU(1)POLY%(0)MU(0)):EF%(4)POLY%(2)MU(2)$EF%(5)(POLY%(0))(MU(0)):EF%(6)(POLY%(0))(MU(0)):EF%(7)POLY%(1)MU(1)')EF%"----------------------------------------"A34,6:10::34,0\ 7::"WORK SPACE"::CF%Ė11:22000:HELP%OK%D(2)MU(2):D(1)MU(1):D(0)MU(0):20:" = ";:10000:1050 CF%Ė4:20000:HELP%OK%D(2)MU(2):D(1)MU(1):D(0)MU(0):19:" =(NU$)%HQQ17:TE%(QQ)0:QQ:TE%0< DO N% PROBLEMS.eP1N%:QQ17:E%(QQ)0:QQ:QUIT%0T%2000,3000,4000,5000:T%5ĴR(5)2000,3000,3000,4000,5000::"FACTOR":D(2)POLY%(2):D(1)POLY%(1):D(0)POLY%(0):3:15:10000+::176:QQ1QQ6QQ6N%0790816368,0:QQ6T%QQMQQ6ė:45000: :16:4:"ENTER THE NUMBER AND PRESS ";::"RETURN";::".":10:"HOW MANY PROBLEMS (1 TO 10)? ";NU$*(NU$)28004(NU$)((NU$))(NU$)1(NU$)10800>N%RATIC TRINOMIALS":<4:"2. HARD QUADRATIC TRINOMIALS":e4:"3. DIFFERENCE OF TWO SQUARES":4:"4. COMMON FACTOR":4:"5. MIXED PROBLEMS":N%0Ė4:"6. EXIT PROGRAM"20:8:"YOUR SELECTION: "; 16368,0QQ(16384)O YOU WANT INSTRUCTIONS (Y OR N)? ";d QQ(1):QQ(16384)128:QQ78QQ110QQ89QQ121670 16368,0:QQ97QQQQ32 QQ89İ60000 :"OKAY, ";N$;". HERE WE GO.": "WHAT KIND OF PROBLEMS DO YOU WANT?":::4:"1. EASY QUADDENT'S NAME. b:9:"PLEASE ENTER YOUR FIRST NAME (UP TO NINE":"CHARACTERS) AND PRESS ";::"RETURN";::".":13:"NAME: ";N$ l vN$""610 (N$)10N$(N$,10):::"I'LL CALL YOU ";N$;" FOR SHORT.":30000 :9:"HI, "N$"."$ 11:"DNEXT TO SOLVE X+2 YOU WOULD"#Kk;Kt"CHOOSE OPTION 2."GK~2590:\K"GOOD LUCK!!!!"kK'2590:260S..."::1JB"1) ADD SAME NUMBER TO BOTH SIDES"`JU"2) SUBTRACT SAME NUMBER FROM BOTH SIDES"JV"3) MULTIPLY BOTH SIDES BY SAME NUMBER"J`"4) DIVIDE BOTH SIDES BY SAME NUMBER"Ja::"FIRST, TO SOLVE X-6 YOU WOULD CHOOSE"JbKj"OPTION 1. I4I:"HERE YOUR BEST CHOICE WOULD BE TO SET":IhI"EACH FACTOR = 0 AND SOLVE -- OPTION 3."tI$2590:I.:"WORK AREA";::" ( X-6 )( X+2 ) = 0"I8"----------------------------------------" J9::"YOU WILL HAVE THE FOLLOWING CHOICE-- ONE"!H"AFTER EACH PROMPT."-H2590:RH"THESE WILL BE YOUR OPTIONS:":H"ENTER ONE OF THE FOLLOWING: (* TO QUIT)"HH" 1) DIVIDE BOTH SIDES BY A NUMBER"H" 2) FACTOR THE LEFT SIDE"H" 3) SET EACH FACTOR = 0 AND SOLVE"----------------------------------------"\G::"YOU WILL THEN BE PROMPTED AS FOLLOWS..."dG:G"ENTER FIRST FACTOR :"::"ENTER SECOND FACTOR:"G2590G:"YOU MUST ENTER THE FACTORS IN AX+B FORM."H"FOR EXAMPLE, YOU TYPE X-6 AND X+2 M LEFT."&50000:1030+&EF%(7)1900=&E%(7)E%(7)1g&12:"CLOSE, ";N$;", BUT NO CIGAR.":&&"TO GET THE MIDDLE TERM TO MATCH, YOU":&0"MUST MAKE SURE THAT THE SUM OF THE":&:"PRODUCTS OF THE INNER AND OUTER TERMS":'DM0%1ĺ"TI GET THE CORRECT CONSTANT TERM, THE":W%"PRODUCT OF THE CONSTANTS IN THE FACTORS":%M0%1ĺ"TIMES THE ";M0%;" YOU FACTORED OUT":%"MUST BE EQUAL TO ";POLY%(0);".";%EF%(7)1790&" FIX THIS TERM,"::"AND YOU JUST HAVE THE MIDDLE TER"::"WELL AS THE WRONG VALUE."::EF%(7)1670$"IF YOU FIX BOTH OF THESE ERRORS, THEN"::"GETTING THE MIDDLE TERM WILL BE"::"THE LAST STEP."$50000:1030$EF%(6)1800$E%(6)E%(6)1$12:"YOU'RE NOT QUITE RIGHT, ";N$;".":&%"TOHAVE DIFFERENT SIGNS: ONE POSITIVE"::"AND ONE NEGATIVE.";N#rEF%(7)1670#w" ONCE YOU CORRECT THE"::"SIGN, YOU CAN WORK ON THE LINEAR TERM.":1670/$|E%(6)E%(6)1:N$;", YOU HAVE MADE TWO MISTAKES."::"THE CONSTANT TERM HAS THE WRONG SIGN AS::"THE CONSTANT TERMS IN THE FACTORS MUST":v"^"HAVE THE SAME SIGN: BOTH POSITIVE"::"OR BOTH NEGATIVE.";:1650"c12:"THAT ISN'T CORRECT, ";N$;".":"h"SINCE THE CONSTANT TERM IS NEGATIVE,"::"THE CONSTANT TERMS IN THE FACTORS MUST":<#m"!6"CORRECT THESE ERRORS BEFORE YOU TRY TO"::"GET THE RIGHT MIDDLE TERM."]!;50000:1030o!@EF%(5)1700!EE%(5)E%(5)1!JEF%(6)1660!O(POLY%(0))11635!T12:"THAT ISN'T CORRECT, ";N$;".":."Y"SINCE THE CONSTANT TERM IS POSITIVE,""IS INCORRECT.":# "EF%(7)1595- '1590v ,E%(5)E%(5)1:E%(6)E%(6)1:"YOU HAVE MADE THREE ERRORS, ";N$;".": 1"THE ";:D(2)1:D(1)0:D(0)0:10000:" TERM IS WRONG, AND THE CONSTANT"::"TERM IS WRONG IN BOTH SIGN AND VALUE."::EF%(7)1595LE TERM.";:1595'EF%(5)EF%(6)1580"WELL, ";N$;", I SEE TWO PROBLEMS."::"FIRST, THE ";:D(2)1:D(1)0:D(0)0:10000:" TERM IS WRONG. SECOND,":"THE CONSTANT TERM ";:EF%(5)E%(5)E%(5)1:"HAS THE WRONG SIGN."::1570 E%(6)E%(6)1:00:" TERM, THE PRODUCT OF THE":K"COEFFICIENTS OF X IN THE FACTORS":M0%1ĺ"AND THE ";M0%;" WHICH YOU HAVE FACTORED OUT":"MUST BE EQUAL TO ";POLY%(2);".";EF%(7)1595 " ONCE YOU GET THE"::"FIRST TERM, YOU CAN FIX THE MIDDL ";:D(2)0:D(1)R%(1):10000:", AND ":X"THE SQUARE ROOT OF ";T2%;" IS ";R%(0);"."i50000:1030{EF%(4)1600E%(4)E%(4)1EF%(5)EF%(6)1550"YOU'RE A LITTLE OFF, ";N$;". TO GET":!"THE RIGHT ";:D(2)1:D(1)0:D(0)0:100THOD FOR THIS KIND OF PROBLEM.":1499M"YOU'RE CLOSE, BUT YOU HAVE THE":T1%POLY%(2):T2%POLY%(0):M0%0M0%1T1%T1%M0%:T2%T2%M0%("WRONG FACTORS. LET ME GIVE YOU A HINT."::"THE SQUARE ROOT OF ";:D(2)T1%:D(1)0:D(0)0:10000:" ISSWER."_50000:1030)xEF%(3)1500;E%(3)E%(3)1e"I'M AFRAID THAT'S WRONG, ";N$;".":wMU(1)01460"IF YOU LOOK CAREFULLY, YOU'LL NOTICE"::"THAT THIS IS A DIFFERENCE OF TWO SQUARES"%"PROBLEM. YOU MUST USE A SPECIAL"::"ME1375UE%(3)E%(3)1:12:"I CAN SEE TWO MISTAKES, ";N$;"."::"YOU DIDN'T FACTOR OUT THE RIGHT COMMON"::"FACTOR, AND YOU DIDN'T USE THE PROPER"::"METHOD FOR A DIFFERENCE OF TWO SQUARES."Z:"IF YOU FIX THESE ERRORS, YOU'LL HAVE"::"THE RIGHT AN.":1355(A12:"NOT QUITE, ";N$;".":pF"THE TERMS OF THIS POLYNOMIAL DON'T"::"HAVE ANY COMMON FACTORS."KEF%(0)1ĺ:"FIND THE RIGHT FACTOR, AND YOU'RE DONE.":1375P:"GET THIS PART RIGHT, THEN WORRY"::"ABOUT THE REST OF THE PROBLEM.": RIGHT, I WILL TELL YOU SO.":15:"IF YOU ARE WRONG, I WILL POINT OUT YOUR ":"MISTAKE AND GIVE YOU ANOTHER CHANCE."o,50000:pT5:"IF YOU NEED HELP, PRESS THE ";::"H";::" KEY.":8:"I WILL HELP YOU BY KEEPING TRACK OF THE ":"PRODUCT AS YOU CHAERS."n50000:n9:"IF YOU MAKE A MISTAKE, MOVE THE CURSOR ":"OVER THE ERROR, ERASE IT WITH THE SPACE ":"BAR, AND ENTER THE CORRECTION."n50000:n5:"WHEN YOU FINISH FACTORING, PRESS THE "::"RETURN";::" KEY."to11:"IF YOU AREN(36)START%120220,20210,20220,20210,20210,20210,20230,20220,20210,20220,20210,20210,20210,20290,20290u6N202906N36,(36)1:6N36,(36)2:6O36,(36)3:6BO7LO(36)START%120310,20390,20320,20390,20390,20330,20340,20390,20390,2035:"YOU UNTIL YOU FINISH WORKING.":50000G5N34,15:23::34,0:200065N(36)START%120190,20190,20190,20110,20120,20110,20110,20110,20120,20130,20110,20120,20110,20110,201105N201905N36,(36)1:5N36,(36)2:5N36,(36)3:5Nj6YS HIT S.":50000:200954uNHELP%1:"ALL RIGHT, ";:N$;"."::"TO HELP YOU, I'LL KEEP TRACK OF THE"::"PRODUCT AS YOU CHANGE THE FACTORS.":50000)5zN34,15:23::34,0:"I WON'T TELL YOU IF YOU'RE RIGHT OR"::"WRONG, AND MISTAKES WON'T COUNT AGAINST":M$"q"ġ:P17:TE%(P)TE%(P)E%(P):TE%TE%E%(P):P:QUIT%1:1950^3fNM$"H"M$"h"20020u3kN34,15:23::34,04pNHELP%ĺ"SORRY, ";N$;"."::"I CAN'T HELP YOU ANY MORE WITHOUT"::"TELLING YOU THE ANSWER. IF YOU'RE"::"REALLY STUCK, YOU CAN ALWACNM$(8)İ20100&2HNM$(21)İ20200B2MNM$"0"M$"9"İ203002RNM$(13)(M0%M1%(1)1M2%(1)1S1%S2%C1%(1)1C1%(2)1C2%(1)1C2%(2)1)Ĺ34,13:23::34,0:V%1:2WNM$"+"M$"-"İ205002\NM$"S"M$"s"İ55000:20000C3aNM$"Q"UTION."::18::"Q";::" TO QUIT.";:V%1:START%1R1(NM$"H"M$"h"ĖSTART%3k1)NHELP%İ21000:200201*N" ( X )( X )";:36,START%2:OK%0:M0%0:M1%(1)1:M2%(1)1:S1%0:S2%0:C1%(1)1:C1%(2)1:C2%(1)1:C2%(2)114NM$1>NM$" "İ2060020#N PRODUCT.20%NV%(37):START%(36):HELP%00&N14:1:"----------------------------------------":6:"USE ARROW KEYS TO MOVE CURSOR."::8:"PRESS: ";::"RETURN";::" WHEN DONE.":51'N18::"H";::" FOR HELP."::18::"S";::" TO SEE SOLIN/: MU(2-0).c/:MU(2)M1%(1)M2%(1):MU(1)M1%(1)M2%(0)M1%(0)M2%(1):MU(0)M1%(0)M2%(0)/:M0%0M0%1MU(2)M0%MU(2):MU(1)M0%MU(1):MU(0)M0%MU(0)/:/ N ENTER SUBROUTINE/!N SET HELP% TO NON-ZERO/"N TO DISPLAY RUNNINGD(0)0(D(2)0D(1)0)ĺ"+";).'D(0);G.<(D(2)0D(1)0D(0)0ĺ0;M.(h.: MULTIPLY SUBROUTINE.: PASS COEFFICIENTS OF.: FACTORS IN.: M1%(1-0), M2%(1-0).: PASS CONSTANT FACTOR.: (IF ANY) IN M0%./: RESULT RETURNED PLAY SUBROUTINE4-' PASS COEFFICIENTS OF POLY. ING-' D(2-0)Y-'D(2)010100m-$'D(2)1ĺD(2);-.'"X";:(37):2;(10);-t'D(1)010200-~'D(1)0D(2)0ĺ"+";-'(D(1))1ĺD(1);-'D(1)1ĺ"-";-'"X";-'D(0)010300.'LEM.u,D2%0:CF%1:M0%R(9):FX%0:M1%(1)0:M1%(0)1:M2%(1)R(3):M2%(0)R(9):M2%(0)M2%(1)(M2%(0)M2%(1))5010,R(2)2FX%1:M1%(1)1:M1%(0)0,FX%M0%15010,15000,POLY%(2)MU(2):POLY%(1)MU(1):POLY%(0)MU(0):F0%M0%:-' DIS4010+M0%R%(1)294010V+(LC1%(M0%1R%(1)1))(LC1%M0%1R%(1)1)4010^+QQ+M1%(1)R%(1):M2%(1)R%(1):M1%(0)R%(0):M2%(0)R%(0)+15000+POLY%(2)MU(2):POLY%(1)MU(1):POLY%(0)MU(0):F0%M0%:, CREATE A COMMON FACTOR PROB2%(0))(M1%(1)1M2%(1)1M0%1)30100* 15000k* POLY%(2)MU(2):POLY%(1)MU(1):POLY%(0)MU(0):F0%M0%:* CREATE A DIFFERENCE OF SQUARES PROBLEM.*LC1%LC1%+D2%1:CF%0:M0%1:R%(1)R(3):R%(0)R(9):QQ2R%(1):DIVQQ(R%(1))DIVQQ(R%(0))TRINOMIAL PROBLEM.n) D2%0:CF%0:M0%1:M1%(1)R(3):M2%(1)R(3):M1%(0)R(9)SIGN(0):M2%(0)R(9)SIGN(0)) M0%M1%(1)M2%(1)43010) QQ29:DIVQQ(M1%(1))DIVQQ(M1%(0))DIVQQ(M2%(1))DIVQQ(M2%(0))3010) QQ%* (M1%(1)M2%(1)M1%(0)MAKDOWN.(20:700=( CREATE AN EASY TRINOMIAL PROBLEM.(D2%0:CF%0:F0%0:M0%0:M1%(1)1:M2%(1)1:M1%(0)R(9)SIGN(0):M2%(0)R(9)SIGN(0):M1%(0)M2%(0)2010(15000(POLY%(2)MU(2):POLY%(1)MU(1):POLY%(0)MU(0):) CREATE A HARD NGE THE FACTORS.p^14:"IF YOU CANNOT SOLVE A PROBLEM, PRESS"::"THE ";::"S";::" KEY. I WILL THEN SHOW YOU HOW TO"::"FACTOR THE POLYNOMIAL."ph50000:qr2:"ASKING FOR HELP DOES NOT COUNT AGAINST ":"YOU. DON'T BE AFRAID TO USE THESE 36)START%1ı*FXXF%1:C1%(2)1:"X(";NFX23000: DIGEST NEW INFORMATIONTFX~FY CHECK TO SEE THAT FACTORS ARE GOOD.FYHELP%T1%(36):T2%(37):T2%:36,START%9:10):T2%1:36,START%9:13);:36,T1%:37,T2%FYXF%23030FYM1%(1)0%G0,22640,22650,22660,22690$EMX22690?ERXC1%(1)1:" ";:22680aE\XXF%0:C1%(2)1:" (";:22680|EfXM2%(1)1:" X";:22680EpXS2%0:" ";:22680EzXC2%(1)1:" ";:22680EXC2%(2)1:" ";(8);:22680EX23000: DIGEST NEW INFORMATIONEXFX(22380D?WM$;"X";:223806DDWC2%(1)(M$):M$;:22380XDNWC2%(2)(M$):M$;(8);:22380|DlW23000: DIGEST NEW INFORMATIONDvWDW(36)START%5ıDWM$"+"S2%1:22530DWS2%1DXM$;:23000:EHX(36)START%122610,22620,22690,22630,22692210,22290,22290CV22290-CV36,(36)1:?CV36,(36)2:ECWCW(36)START%122310,22320,22390,22330,22390,22390,22340,22350,22390C!W22390C&WC1%(1)(M$):M$;:22380C0WXF%0:C1%(2)(M$):M$;"(";:22380D:WM2%(1)(M$):M$"1"ĺ" X";::"YOU UNTIL YOU FINISH WORKING.":50000GBOV34,15:23::34,0:22006BTV(36)START%122190,22110,22110,22120,22110,22120,22110,22110,22110BYV22190B^V36,(36)1:BhV36,(36)2:BVCV(36)START%122210,22220,22210,22220,22210,22210,2YS HIT S.":50000:22095AEVHELP%1:"ALL RIGHT, ";:N$;"."::"TO HELP YOU, I'LL KEEP TRACK OF THE"::"PRODUCT AS YOU CHANGE THE FACTORS.":50000)BJV34,15:23::34,0:"I WON'T TELL YOU IF YOU'RE RIGHT OR"::"WRONG, AND MISTAKES WON'T COUNT AGAINST":M$"q"ġ:P17:TE%(P)TE%(P)E%(P):TE%TE%E%(P):P:QUIT%1:1950^@6VM$"H"M$"h"22020u@;V34,15:23::34,0A@VHELP%ĺ"SORRY, ";N$;"."::"I CAN'T HELP YOU ANY MORE WITHOUT"::"TELLING YOU THE ANSWER. IF YOU'RE"::"REALLY STUCK, YOU CAN ALWA0?VM$(21)İ222002?VM$"0"M$"9"İ22300L?VM$"X"M$"x"İ22700?"VM$(13)(M0%M2%(1)1XF%S2%C1%(1)1C1%(2)1C2%(1)1C2%(2)1)Ĺ34,13:23::34,0:V%1:?'VM$"+"M$"-"İ22500?,VM$"S"M$"s"İ55000:22000C@1VM$"Q""S";::" TO SEE SOLUTION."::14:"HIT ";::"Q";::" TO QUIT.";:V%1:START%1l>UHELP%İ23000:22020>U" ( X )";:36,START%:OK%0:M0%0:M2%(1)1:S2%0:XF%0:C1%(1)1:C1%(2)1:C2%(1)1:C2%(2)1>VM$>VM$" "İ22600?VM$(8)İ2210=U ENTER2 SUBROUTINE:=UV%(37):START%(36):HELP%0=U14:1:"----------------------------------------":6:"USE ARROW KEYS TO MOVE CURSOR."::10:"HIT ";::"RETURN";::" WHEN DONE.":S>U13:"HIT ";::"H";::" FOR HELP."::10:"HIT ";::C2%(2)^TZ׺"OF EACH TERM OF THE POLYNOMIAL."::"THEREFOR368,0Râ24:10:23);RñCRֲ SHOW HOW TO FACTOR EXPRESSION\R֗:"OKAY, ";N$;".":Rֺ"I'M GOING TO SHOW YOU HOW TO FACTOR":Rֺ"THIS POLYNOMIAL.":50000:Sח::"FACTOR"::ZZ02:D(ZZ)POLY%(ZZ):ZZ:3:15:10000:::"----------------- GUESS IT'S TIME FOR YOU TO MOVE ON":WQ2:"TO BIGGER AND BETTER THINGS. GOODBYE."]QyQPò SUBROUTINE: WAIT FORQZò USER TO HIT RETURN.Qnâ24:8:"PRESS ";::"RETURN";::" TO CONTINUE. ";Qxù16368,0Qí(16384)1281350050Rù16 ";TE%Pœ50000:LPȯ:10:(21(N$))2:"THAT'S ALL FOR NOW, ";N$;".":tPү7:"THANKS FOR WORKING WITH ME.":PׯPC10:N%0PCTE%N%PܯN%4PC.25T%5QUIT%Ė10:"COME BACK AGAIN SOON."::7:"WE'LL DO SOME MORE PROBLEMS.":45050&Q毖3:"ITWO SQUARES ... ";TE%(3):IO"LEADING COEFFICIENT ......... ";TE%(4):xO"SIGN OF CONSTANT TERM ....... ";TE%(5):O"CONSTANT TERM ............... ";TE%(6):O"LINEAR TERM ................. ";TE%(7)O:P"GRAND TOTAL ................. FOR ALL PROBLEMS.7NJ:11:"TOTAL ERROR SUMMARY"::aNT" ERROR NUMBER"N^" ----- ------":Nh"INCORRECT FORMAT OF FACTORS . ";TE%(1):Nr"FINDING COMMON FACTORS ...... ";TE%(2):O|"DIFFERENCE OF M ................. ";E%(7)_ME%0:T117:TE%(T1)TE%(T1)E%(T1):E%E%E%(T1):T1:TE%TE%E%gM:M"TOTAL ....................... ";E%::M䉭E%2E%2MME$(3E%(3(1)))MH50000:M@ TOTAL ERRORSMA PRINTS ERROR SUMMARYNB ";E%(1):7L"FINDING COMMON FACTORS ...... ";E%(2):eLꈺ"DIFFERENCE OF TWO SQUARES ... ";E%(3):L"LEADING COEFFICIENT ......... ";E%(4):L"SIGN OF CONSTANT TERM ....... ";E%(5):L"CONSTANT TERM ............... ";E%(6):M"LINEAR TER-- 2 SEC.K:uDD11630:DD:7K ERROR SUBROUTINE.SK PRINTS ERROR SUMMARYlK FOR THIS PROBLEM.K UPDATES TOTALS.Kˆ:" ERROR NUMBER"K̈" ----- ------": Lֈ"INCORRECT FORMAT OF FACTORS . (M1%(0));:(M1%(0))10ĺ" ";'JHb")";HJpb"(";:M2%(1)1ĺ" ";:25220UJzbM2%(1);_Jb"X";zJbM2%(0)0ĺ"+";:25250Jb"-";Jb(M2%(0));:(M2%(0))10ĺ" ";Jb") = ";JbD(2)MU(2):D(1)MU(1):D(0)MU(0):10000J8c K0u DELAY SUBROUTINE :10000:36,T1%:(Ia SHOW SUBROUTINEIIa DISPLAYS A MULTIPLICATIONiIa VARIABLES AS IN MULTIPLYtIa15000IaM0%0M0%1ĺ" ";:25100IaM0%;I b"(";:M1%(1)1ĺ" ";:25120IbM1%(1);I b"X";I*bM1%(0)0ĺ"+";:25150I4b"-";J>b1M2%(0)C2%(2):230902HZM2%(0)10C2%(1)C2%(2)QH2ZLF%M1%(0):XF%LF%M1%(1)H"A SOLUTION."_H50000 `FC1N1%:M1%(1)FA%(1,FC,0):M2%(1)FASO POSITIVE";:58040%^"NEGATIVE";_^", THE"::"CONSTANTS IN THE FACTORS MUST BOTH BE":z^RE%(1)0ĺ"POSITIVE."^RE%(1)0ĺ"NEGATIVE."^50000:58400^"SINCE THE LAST TERM IS NEGATIVE,":^"THE CONSTANTS IN THE FACTORS MUST":(_4,153 23:10:"PRESS THE MINUS KEY <->.":9:15I G$:G$"-"1190u G$;::23:13:"NOW PRESS <6>.":9:16 G$:G$"6"2010 G$;:20:"= X";:8:"2";:9:"-11X+30":34,12: 15:15:"WELL DONE!":18:" YOU'VE COMPLETED THE SAMPLE PRESS <5>.":9:9& `G$:G$"5"1120 jG$;::"NOW WE MUST MOVE THE CURSOR AGAIN.":23:4:"PRESS THE RIGHT ARROW KEY TWICE.":9:10 tG$:G$(21)1140 ~" ";:13 G$:G$(21)1160 " ";:34,13::"THE SECOND FACTOR IS ( X-6 )."::3ACTORS IN.":100? $:"THE FIRST FACTOR IS ( X-5 ).":34,15: .21:"TO MOVE THE CURSOR, PRESS THE RIGHT"::"ARROW KEY.":9:6 8G$:G$(21)1080 B:23:7:"NOW PRESS THE MINUS KEY <->.":9:8 LG$:G$"-"1100 VG$;::23:14:"NOW P---------------------------":34,13 14:" THE CURSOR WILL APPEAR INSIDE THE"::"PARENTHESES. THIS IS WHERE YOU WILL"::"ENTER YOUR FACTORS.":100 :" THE FACTORS FOR THIS EQUATION ARE"::"( X-5 ) AND ( X-6 ). NOW YOU MUST"::"TYPE THE F7:N$", ":3:"LET'S USE AN EASY QUADRATIC TRINOMIAL"::"AS OUR SAMPLE PROBLEM.":100 :"SAMPLE":16:"2"::"FACTOR";::15:"X -11X+30":"----------------------------------------"# ::"WORK SPACE":::5:"( X )( X )":12:"-------------X  FACTORING: SAMPLE PROBLEM? BY KEVIN VESSIO 9/13/84MI0:N$""~II1:IN(768I):IN01000:N$N$(IN):25c PRESS RETURNd24:9:"PRESS ";::"RETURN";::" TO CONTINUE.";:16368,0i(16384)12813105nX 34,0::     .j"ANY FACTOR MUST HAVE THE FORM AX+B,":St"WHERE A AND B ARE INTEGERS.":d~50000:1030sCF%1300EF%(0)EF%(2)0FX%XF%LF%F0%1900E%(2)E%(2)1LF%1XF%ĺ"YOU'RE NOT BEING CAREFUL, ";N$;"."::"DON'T FORGET THAT THE TMU(2)POLY%(1)MU(1)POLY%(0)MU(0)):EF%(4)POLY%(2)MU(2)$EF%(5)(POLY%(0))(MU(0)):EF%(6)(POLY%(0))(MU(0)):EF%(7)POLY%(1)MU(1))EF%(0)0:QQ17:EF%(0)EF%(0)EF%(QQ):QQLEF%(1)1200VE%(1)E%(1)1`16:"SORRY, ";N$;".":11:22000:HELP%OK%D(2)MU(2):D(1)MU(1):D(0)MU(0):20:" = ";:10000:1050CF%Ė4:20000:HELP%OK%D(2)MU(2):D(1)MU(1):D(0)MU(0):19:" = ";:1000012:1=EF%(1)OK%:EF%(2)(F0%0M0%1F0%1M0%0F0%M0%):EF%(3)D2%(POLY%(2)4000,5000:T%5ĴR(5)2000,3000,3000,4000,5000S:"PROBLEM #"P:::"FACTOR":D(2)POLY%(2):D(1)POLY%(1):D(0)POLY%(0):3:15:100001:4:"----------------------------------------"34,6:10::34,0 7::"WORK SPACE"::PCF%ĭQQ6ė:45000:i :4:N$","::"YOU MAY TRY UP TO 9 PROBLEMS."::"HOW MANY WOULD YOU LIKE? ";:G$""*G$:N%(G$):N%08104G$;HQQ17:TE%(QQ)0:QQ:TE%0 DO N% PROBLEMS.P1N%:QQ17:E%(QQ)0:QQ:QUIT%0/T%2000,3000,:"3. DIFFERENCE OF TWO SQUARES":?4:"4. COMMON FACTOR":]4:"5. MIXED PROBLEMS":~N%0Ė4:"6. EXIT PROGRAM"20:8:"YOUR SELECTION: ";:G$"" G$:QQ(G$):QQ0QQ6765G$;QQ1QQ6QQ6N%0780QQ6T%QQ(79))16:XX(XX):G$"Y"G$"y"ī60000:700GG$"N"G$"n"670PG$;w:3:QQ19:K1%(QQ)0:K2%(QQ)0:"WHAT KIND OF PROBLEMS DO YOU WANT?":::4:"1. EASY QUADRATIC TRINOMIALS":4:"2. HARD QUADRATIC TRINOMIALS":"48)" "(8);:ZZ16086{N$(N$,(N$)1):ZZZZ1:610:3:"HI, "N$"!"::"THIS PROGRAM WILL HELP YOU PRACTICE"::"FACTORING DIFFERENT KINDS OF ALGEBRAIC"::"EXPRESSIONS."::13:"DO YOU WANT INSTRUCTIONS (Y OR N)? ";:G$"".G$:XX((78)ETTERS) AND PRESS .":::10)"NAME: ";I`ZZ0:N$"":G$"":ZH0kbG$:ZH(G$):ZH13ZZ0650ydZH8630gZZ10610iZH65ZH122610jZH90ZH97610lZH90G$(ZH32)qN$N$G$:G$;:ZZZZ1:610vZZ0610x(C EXPRESSIONS"::4 10:12:"DESIGN BY DON ROSS"\ 12:10:"PROGRAM BY MARK BERMAN": 10:"MICROCOMPUTER WORKSHOPS": 17:"(C) 1983" &30000:30000 X GET STUDENT'S NAME./]:3:" PLEASE ENTER YOUR FIRST NAME (UP TO"::" TEN L* ME$(7)"KEEP TRYING. YOU'LL GET IT."_ ME$(8)"DON'T BE DISCOURAGED. YOU'LL DO BETTER."t (769)060800  PRINT A TITLE PAGE. ::ZZ140:1:ZZ:" ";:23:ZZ:" ";::ZZ122:ZZ:1:" ";:40:" ";:: 6:6:"FACTORING ALGEBRAI SEE YOU'VE BEEN DOING YOUR HOMEWORK!"X xME$(2)"TOO BAD YOUR TEACHER CAN'T SEE THIS!" ME$(3)"WELL, WE CAN'T ALL BE PERFECT." ME$(4)"THAT WAS A GOOD TRY." ME$(5)"YOU ALMOST MADE IT ON THAT ONE." ME$(6)"THESE PROBLEMS ARE NOT SO EASY."%(1),RE%(2)J FR(X)(X(1)1): RETURN RANDOM NUMBER BETWEEN 1 AND X PSIGN(X)(2R(2))3: RETURN RANDOM SIGN, 1 OR -1 ZDIVQQ(X)(XQQ)(XQQ): RETURNS 1 IF X IS A MULTIPLE OF QQ, 0 IF NOT. dME$(0)"VERY IMPRESSIVE!"& nME$(1)"IEENS, REFORMAT ERROR SUMMARY & ANALYSIS, FIX INPUT FACTORS ROUTINE, RANDOM ## GENERATOR, SOLUTION ROUTINE, INSTRUCTIONS, COMMON FACTORS ROUTINES,.... <K1%(9),K2%(9),C1%(2),C2%(2),D(2),E%(7),EF%(7),FA%(1,6,1),TE%(7),M1%(1),M2%(1),ME$(8),MU(2),POLY%(2),Rj 33,40 FACTORING. VERSION 1.1J COPYRIGHT (C) 1983 BYh( MICROCOMPUTER WORKSHOPS~2 PORTCHESTER, NY3 LAST UPDATE: 9/13/844 BY: KEVIN VESSIO 5 UPDATED THE FOLLOWING: CHANGED ALL INPUTS TO GETS, REFORMAT MOST SCR          !!! ! ! ! ! !!!!!!!!!""" " " " " """""""""                      T THE"::"SIGN, YOU CAN WORK ON THE LINEAR TERM.":1670&|E%(6)E%(6)1:N$;", YOU HAVE MADE TWO MISTAKES."::"THE CONSTANT TERM HAS THE WRONG SIGN AS"::"WELL AS THE WRONG VALUE."::EF%(7)1670/'"IF YOU FIX BOTH OF THESE ERRORS, THEN"::"GETTIEGATIVE.";:16509%c12:"THAT ISN'T CORRECT, ";N$;".":%h"SINCE THE CONSTANT TERM IS NEGATIV,"::"THE CONSTANT TERMS IN THE FACTORS MUST":%m"HAVE DIFFERENT SIGNS: ONE POSITIVE"::"AND ONE NEGATIVE.";%rEF%(7)16708&w" ONCE YOU CORREC%(5)1700$EE%(5)E%(5)1,$JEF%(6)1660E$O(POLY%(0))11635n$T12:"THAT ISN'T CORRECT, ";N$;".":$Y"SINCE THE CONSTANT TERM IS POSITIVE,"::"THE CONSTANT TERMS IN THE FACTORS MUST":%^"HAVE THE SAME SIGN: BOTH POSITIVE"::"OR BOTH NRORS, ";N$;".":#1"THE ";:D(2)1:D(1)0:D(0)0:10000:" TERM IS WRONG, AND THE CONSTANT"::"TERM IS WRONG IN BOTH SIGN AND VALUE."::EF%(7)1595#6"CORRECT THESE ERRORS BEFORE YOU TRY TO"::"GET THE RIGHT LINEAR TERM."#;50000:1030 $@EF)1:D(1)0:D(0)0:10000:" TERM IS WRONG. SECOND,":""THE CONSTANT TERM ";:EF%(5)E%(5)E%(5)1:"HAS THE WRONG SIGN."::1570"E%(6)E%(6)1:"IS INCORRECT.":""EF%(7)1595"'1590#,E%(5)E%(5)1:E%(6)E%(6)1:"YOU HAVE MADE THREE ER;" WHICH YOU HAVE FACTORED OUT":H!"MUST BE EQUAL TO ";POLY%(2);".";Z!EF%(7)1595! " ONCE YOU GET THE"::"FIRST TERM, YOU CAN FIX THE LINEAR TERM.";:1595!EF%(5)EF%(6)15806""WELL, ";N$;", I SEE TWO PROBLEMS."::"FIRST, THE ";:D(2030 EF%(4)1600' E%(4)E%(4)1? EF%(5)EF%(6)1550m "YOU'RE A LITTLE OFF, ";N$;". TO GET": "THE RIGHT ";:D(2)1:D(1)0:D(0)0:10000:" TERM, THE PRODUCT OF THE": "COEFFICIENTS OF X IN THE FACTORS":!!M0%1ĺ"AND THE ";M0%LY%(0):M0%0M0%1T1%T1%M0%:T2%T2%M0%"WRONG FACTORS. LET ME GIVE YOU A HINT."::"THE SQUARE ROOT OF ";:D(2)T1%:D(1)0:D(0)0:10000:" IS ";:D(2)0:D(1)R%(1):10000:", AND ":"THE SQUARE ROOT OF ";T2%;" IS ";R%(0);"." 50000:1MU(1)01460k"IF YOU LOOK CAREFULLY, YOU'LL NOTICE"::"THAT THIS IS A DIFFERENCE OF TWO SQUARES""PROBLEM. YOU MUST USE A SPECIAL"::"METHOD FOR THIS KIND OF PROBLEM.":1499"YOU'RE CLOSE, BUT YOU HAVE THE":-T1%POLY%(2):T2%POON"::"FACTOR, AND YOU DIDN'T USE THE PROPER"::"METHOD FOR A DIFFERENCE OF TWO SQUARES."Z:"IF YOU FIX THESE ERRORS, YOU'LL HAVE"::"THE RIGHT ANSWER."_50000:1030xEF%(3)1500E%(3)E%(3)1"I'M AFRAID THAT'S WRONG, ";N$;".": FACTORS."KKEF%(0)1ĺ:"FIND THE RIGHT FACTOR, AND YOU'RE DONE.":1375P:"GET THIS PART RIGHT, THEN WORRY"::"ABOUT THE REST OF THE PROBLEM.":1375[UE%(3)E%(3)1:12:"I CAN SEE TWO MISTAKES, ";N$;"."::"YOU DIDN'T FACTOR OUT THE RIGHT COMM12:"SORRY, ";N$;"."::"YOU'VE LEFT OUT AN IMPORTANT STEP.":<"DON'T FORGET THAT ";POLY%(2);", ";POLY%(1);", AND ";POLY%(0)::"HAVE A COMMON FACTOR.":1355A12:"NOT QUITE, ";N$;".": F"THE TERMS OF THIS POLYNOMIAL DON'T"::"HAVE ANY COMMON000:1030EF%(2)1400-E%(2)E%(2)1>EF%(3)1365T#M0%0M0%11335j(F0%0F0%11345-12:"THAT'S NOT RIGHT, ";N$;"."::M0%;" IS NOT THE LARGEST COMMON":2"FACTOR OF ";POLY%(2);", ";POLY%(1);", AND ";POLY%(0);".":1355>7T YOU DID NOT FIND THE LARGEST"::"COMMON FACTOR FOR THIS POLYNOMIAL.":50000:103016:"THAT'S NOT RIGHT, ";N$;"."::"THE TERMS OF THIS POLYNOMIAL ARE NOT"::"ALL DIVISIBLE BY ";D(2)0:D(1)0:D(0)LF%:XF%D(1)D(0):D(0)0  10000:".":50PUTATION.":50000:1030LF%F0%FX%Ģ16:"YOU MADE A SMALL OVERSIGHT, ";N$;"."::"NOTICE THAT X IS ALSO A FACTOR IN EACH"::"TERM OF THIS POLYNOMIAL.":50000:1030T(F0%LF%(F0%LF%)XF%FX%)Ģ16:"YOU'RE ON THE RIGHT TRACK, ";N$;","::"BUERMS OF THIS"::"BINOMIAL HAVE A COMMON FACTOR."::"ONCE YOU REMOVE THAT FACTOR, YOU'LL BE"::"DONE WITH THIS PROBLEM.":50000:1030FX%XF%LF%F0%Ģ16:"VERY CLOSE, ";N$;"."::"YOU FOUND THE RIGHT COMMON FACTOR, BUT"::"YOU MADE AN ERROR IN COM0000'6aNM$"Q"M$"q"ġ:QUIT%1:1950B6fNM$"H"M$"h"20020Y6kN34,15:23::34,06pNHELP%ĺ"SORRY, ";N$;"."::"I CAN'T HELP YOU ANY MORE WITHOUT"::"TELLING YOU THE ANSWER. IF YOU'RE"::"REALLY STUCK, YOU CAN ALWAYS PRESS S.":50000:20095zM$" "İ20600!5CNM$(8)İ2010065HNM$(21)İ20200R5MNM$"0"M$"9"İ203005RNM$(13)(M0%M1%(1)1M2%(1)1S1%S2%C1%(1)1C1%(2)1C2%(1)1C2%(2)1)Ĺ34,13:23::34,0:V%1:5WNM$"+"M$"-"İ205006\NM$"S"M$"s"İ55000:2::"H";::" FOR HELP.";:22::"Q";::" TO QUIT.";:V%1:START%1b4(NM$"H"M$"h"ĖSTART%3{4)NHELP%İ21000:200204*N" ( X )( X )";:36,START%2:OK%0:M0%0:M1%(1)1:M2%(1)1:S1%0:S2%0:C1%(1)1:C1%(2)1:C2%(1)1:C2%(2)144NM$ 5>N(37):START%(36):HELP%0:14:1:"----------------------------------------";3&N16:6:"USE ARROW KEYS TO MOVE CURSOR."::10:"USE SPACEBAR TO ERASE."::17:"PRESS:"::" ";::"RETURN";::" WHEN DONE.";:22::"S";:E4'N" TO SEE SOLUTION"::" ";:MU(2)M1%(1)M2%(1):MU(1)M1%(1)M2%(0)M1%(0)M2%(1):MU(0)M1%(0)M2%(0)2:M0%0M0%1MU(2)M0%MU(2):MU(1)M0%MU(1):MU(0)M0%MU(0)2:2 N ENTER SUBROUTINE2!N SET HELP% TO NON-ZERO2"N TO DISPLAY RUNNING2#N PRODUCT.N3%NV%ĺ"+";1'D(0);/1<(D(2)0D(1)0D(0)0ĺ0;51(P1: MULTIPLY SUBROUTINEl1: PASS COEFFICIENTS OF1: FACTORS IN1: M1%(1-0), M2%(1-0)1: PASS CONSTANT FACTOR1: (IF ANY) IN M0%.1: RESULT RETURNED IN1: MU(2-0).K2ASS COEFFICIENTS OF POLY. IN/0' D(2-0)A0'D(2)010100U0$'D(2)1ĺD(2);p0.'"X";:(37):2;(10);0t'D(1)0102000~'D(1)0D(2)0ĺ"+";0'(D(1))1ĺD(1);0'D(1)1ĺ"-";0'"X";0'D(0)0103001'D(0)0(D(2)0D(1)0)R(9):FX%0:M1%(1)0:M1%(0)1:M2%(1)R(3):M2%(0)R(r):M2%(0)M2%(1)(M2%(0)M2%(1))5010/R(2)2FX%1:M1%(1)1:M1%(0)0/FX%M0%15010/15000/POLY%(2)MU(2):POLY%(1)MU(1):POLY%(0)MU(0):F0%M0%:/' DISPLAY SUBROUTINE0' P(1)R%(1):M2%(1)R%(1):M1%(0)R%(0):M2%(0)R%(0)_.QQ1P:R%(0)K1%(QQ)R%(1)K2%(QQ)4010.:K1%(P)R%(0):K2%(P)R%(1).15000.POLY%(2)MU(2):POLY%(1)MU(1):POLY%(0)MU(0):F0%M0%:. CREATE A COMMON FACTOR PROBLEM.]/D2%0:CF%1:M0%M0%:4- CREATE A DIFFERENCE OF SQUARES PROBLEM.C-LC1%LC1%-D2%1:CF%0:M0%1:R%(1)R(3):R%(0)R(9):QQ2R%(1):DIVQQ(R%(1))DIVQQ(R%(0))4010-M0%R%(1)294010-(LC1%(M0%1R%(1)1))(LC1%M0%1R%(1)1)4010-QQ1.M1%SIGN(0)&, M0%M1%(1)M2%(1)43010t, QQ29:DIVQQ(M1%(1))DIVQQ(M1%(0))DIVQQ(M2%(1))DIVQQ(M2%(0))3010|, QQ, (M1%(1)M2%(1)M1%(0)M2%(0))(M1%(1)1M2%(1)1M0%1)3010, 15000- POLY%(2)MU(2):POLY%(1)MU(1):POLY%(0)MU(0):F0%(1)1:M1%(0)R(9)SIGN(0):M2%(0)R(9)SIGN(0):M1%(0)M2%(0)2010Q+15000+POLY%(2)MU(2):POLY%(1)MU(1):POLY%(0)MU(0):+ CREATE A HARD TRINOMIAL PROBLEM., D2%0:CF%0:M0%1:M1%(1)R(3):M2%(1)R(3):M1%(0)R(9)SIGN(0):M2%(0)R(9)ʢ16:(31(N$))2:"GOOD WORK, ";N$;".":E*v13:"THAT IS CORRECT."P*50000u*35000: PRINT ERROR BREAKDOWN.|*P*40000: FINAL ERROR BREAKDOWN.*20:650* CREATE AN EASY TRINOMIAL PROBLEM.F+D2%0:CF%0:F0%0:M0%0:M1%(1)1:M2%/)&"TO GET THE LINEAR TERM TO MATCH, YOU":[)0"MUST MAKE SURE THAT THE SUM OF THE":):"PRODUCTS OF THE INNER AND OUTER TERMS":)DM0%1ĺ"TIMES THE FACTOR OF ";M0%;" ";)N"IS ";:D(2)0:D(1)POLY%(1):D(0)0:10000:".")X50000:1030)*lIMES THE ";M0%;" YOU FACTORED OUT":K("MUST BE EQUAL TO ";POLY%(0);".";](EF%(7)1790(" FIX THIS TERM,"::"AND YOU JUST HAVE THE LINEAR TERM LEFT."(50000:1030(EF%(7)1900(E%(7)E%(7)1)12:"CLOSE, ";N$;", BUT NO CIGAR.":NG THE LINEAR TERM WILL BE"::"THE LAST STEP."@'50000:1030R'EF%(6)1800d'E%(6)E%(6)1'12:"YOU'RE NOT QUITE RIGHT, ";N$;".":'"TO GET THE CORRECT CONSTANT TERM, THE":'"PRODUCT OF THE CONSTANTS IN THE FACTORS":$(M0%1ĺ"T