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WJN.JkX"OJ~X NEWSTU v JLslQ3Pe O l5 JDLO F J DLNOAZfM> 5 O $vs_ Yq_f}VYv JLgfv0 0 vO lv2J%L DATEPR O O eI0 |I "OH0 qIWvf> M mM 5  _ Z_ v[ FIXDAT{ qIvO sIe eIvO gIe |IvO 0 ~Ie  GETDATˀ k~ՀDL`O slv lV O `q_vO P O "O gI0 ~I@0 sI O 0 > M 0 5 0 5 p l GET-BOO IB5 ?JpNNHO ?JLJNGWLJ~X0 HWLJNvJ%L MAINSCRι KRwl|~T INITMAINS ]AMAIN.PAKB5 ELEH CH3F5 CCHn INI {Q}~}ā ]A SETUP.DATB5 I]I DL0mN ]A ENTRY.PAK-_!zQvIL a1U About Alge-Blaster Plus v1.0  a2 +Designers: Julie Baumgartner and Anne Hertz a3ڂ *Programmers: David Ely and Louis X. Savain a4 )(c) 1989 by Davidson and Associates, Inc. a5I -Alge-Blaster Plus includes five activities to a6 ,help students learn, practice and review the a7 (topics presented in a first-year Algebra a8 -course. On-line instructions, glossary, hints a9' and an editor are provided. iDraa HpNH(}Z dDra %LM Fm_  Lₑ L LQ L L L L/ i AbtLa sll5  PRT.CA5.FixpatP M p L uLDL/LO /p L Lp DL p L_ Lv V DLNO/9fMM AZfM_ O 5 .$ Lp 5  ?->he^ vH%LV XM p p  O  0 HkX_ 9mV  O  0 HkXHY ?erޅ slHXDV@ml wpC This disk is Write Protected. wpf nHpNH9H  NL M p p NLM %Lsl_ _ %Lml ?wrter O @+O 0 J MvDSetuچ IZ;NI~HNIHN MvUSetu ~HhHhZI;N~HINHINI DL0mN  SETUPDIS' V  Z > fLMY}VM[ setWritf WnO I\䆋C=nO  SU NOV YM V N_ O Z Lq_r0 5 v SU 17fMO Z Lq_r0 5 v SETUPCAOÇ su0+ JDLq_6 sDbD@ _ORq_V vM _ O $V O GO 5 0 rj0 rj0 rj_O d_7f ` O ld_Kf DoSetuS slv5 [V O V LO 2O  RecSiz幈.*RecBuJALLOT .da.dat. .act6..leB..scorN.#.atY.%.corf.'.suq.(.hin}.)#re㈉.rMaxFile.dR_fl矉.una.pBu滉.lPoƉ.pagщ.+lPo܉ ډe  r_ope ~Hn rMak DWHN~HH~XHGNGDO GV D5 L\B D5 V O "vJ vvfE5 JEF5 vE5 C rAddI AG pNG cV DL  %LG DL Ge cDL cL rGetFilev DWGNG> ]O g]0  r_ini AIc c  G vcLL\cDLNc 4cO(cO rfresߊ v rfrop" V O C0 O 5  nupDat3 q_ ~_ O eY}V0lG fbv rfUpDat^ 2c c  NL~HNh rCaO+< 1stNa ‰O V J~HN~HDL  ~H DLNOAZfMM 09fM_ O . ~H L5 p h5 0 LcO 5 0 v~H%L rfċ ĉ N\ ~HN =nO 0vslW0ZDWSZ͋lO l0 5 v rfOpe? 2JEV O ~H2JN rOpe ?HvEV O ~HHN recFli H O v2J%L/0 O HOl| $ NameDateActivityLevelScoreProblems AttemptedProblems CorrectSubjectNumber of Hints tAdJ'.5@HPexgrap蔍J@/@?@O@_@otranJ@/@?@O@_@o@@solvӍJ @/@=@K@Y@g@u@@@mod'J ݍmodAdd9 J L A  Lev14K U M p _  14fM> 5  T$Drak HY xT$Dra HpN nT$Dra "O IÎ  IՎ > O"O]WH~XWHN]WH~X J L ͎ I J 4 WY I U  I: b ͎ J V M _ O 3WY iK m J LO "O0 ,V  > $ uL"OH͉N"OWH~X͉H~X I  Iӏ y ͎ I tO  uL9 NLY I ͎ I'Oڎ$?P؏! ?name/ UV > v V 9 V > OLDV&M HpN MDV5p 5  rdReM 9vfE5 3F5  getRec' vvfE5 J3F5 J  pReƐ 0 Y}VV "O O  M]WH~XDV vtRe slvKG "OPDVKG V 𐮐VlV LO O 0 KG> M0 5 l noRe8  sl&W[ml ShowRe㘑 vH%LƌO &HnO ѐO  @0 C PRTCHRӶ V v V p 5  PTA V ؉LO ؉m > 0 5  PC  Ne ډOI DLYO   PF=  vN  PRTSTk HLV M~ PRTASԁ *OCC PRTAS  * C* C rj H͉NV ͉DLO  ͉v&X0 5 ͉HN BDatڒ  > "O/HkXH͉N >  "O/HkXH͉~X >  lm"OH͉~X͉HN pgHd ډON Alge-Blaster Plus#Davidson & Associates, Inc.CCHHN 's record::Page "OCC*No. Date Level Activity  Subject Problems ScoreCC Bpv : J fMO 5  BsW C b "O J fMO %5  Bsu⅔ - J t O uL9 NLHN ?aLin忔 "O U HpN J 4 WHNƔ]C chkLe N <O qe ~ pvReU  sl4W=ZN剹 ~v ^p CqlO PvRe| vH%LƌO &HnO ѐO  0 C $ĕ To select a menu item: $ 0 Press to enter and leave the menu bar. $$ ! Use  and to select a menu. $` + Use  and  to select an item . $ To select an activity: $Ė 1 Use arrow keys to highlight an icon . $ To exit an activity, press | S. $#   InfoTxNJ -iW͖W,DoInf[ sle v h HpNH8*  9 Zp l5 l DoGlosz WnO $p ValIcn1+ŗJ  MakeBitVa V LO >  p  Set&TestL V $SqH  DoSubSe# O 0 v$S ChkLevSeD q_V OV M _ O R0  SV O fHuL  0 BV O fHuL 0 *V O 0 V O 0 > 5 0 SetupMek v$S$S$S$Sw5  newstu ~HOl| LocalSto0 ZH s_  zzzTestFJ vH%LHuul O 5 H0 ~HJN T1Launch p LvlCtr젙 V O tHSH HvS~ SubCtr췙 hH %|w5  GLaunc HLO p GaLaunc p A1Launc p A2Launc6 p IcnCtrM V  O "5 v/gZHMZH s_ gw5  IcnRtdOAX* IcnGϞ _OV ZH O wO V0  sllLT0 wL graph L MQui hKTWG  EdLaunc pV gridFLI )H +H l| DoStar3 ZH  GetStarN vH%L slllTO HXq0 vvH O X AbtMebOL>L FilMeOL: ̕È% AtvMeOLXmV}L  HlpMeכOLϗ L>L  DVen  BUpVen  MenuPas'OL BVen5 } modKVenT vG V QO V qO 5  PassKedOLLLLL KVen JDLv O 0 nJUO o0 vG 5  main+loo 6Pe jV v V O 5 JDLJDL@ PassIOL\1L#LLL the+loo' vG vx q_ZH uHOV O 5 T0 (_Orj_O q_0 v O w5 G O  GF hKAB+ \=nO TQLQQ^QhK5 j hijklmnopqrstuvwxyz{|}~T,^_ _ @hihiHH^ @@@@ȱHȱhZAHHHH,b @hhh)hYA @ ,b @,^ @ __`H @h^`#`#`@Lb,@@La@]'^p^H^`^:P[M;O@@X@V@W"WOOOQ*SV&SXX{^^^b@dmdNe tnf'`ababeresgoeeghnhvkjjfkDkPkn_Qn$   "$&(*,.02468:<>@BDFHJLNPRTVXZ\^`bdfhjlnprtvxz|~  "$&(*,.02468:<>@BDFHJLNPRTVXZ\^`bdfhjlnprtvxz|~  $(,048<@DHLPTX\`dhlptx|  $(,048<@DHLPTX\`dhlptx|  $(,048<@DHLPTX\`dhlptx|  $(,048<@DHLPTX\`dhlptx| (08@HPX`hpx (08@HPX`hpx (08@HPX`hpx (08@HPX`hpx (08@HPX`hpx (08@HPX`hpx (08@HPX`hpx (08@HPX`hpx 0@P`p 0@P`p 0@P`p 0@P`p 0@P`p 0@P`p 0@P`p 0@P`p 0@P`p 0@P`p 0@P`p 0@P`p 0@P`p 0@P`p 0@P`p 0@P`p  @` @` @` @` @` @` @` @` @` @` @` @` @` @` @` @` @` @` @` @` @` @` @` @` @` @` @` @` @` @` @` @` @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@  !!""##$$%%&&''(())**++,,--..//00112233445566778899::;;<<==>>??  !!!!!!!"""""""#######$$$$((((((((((((((((((((((((((((((((PPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP                        QE%QE%鑄QE%Q%鑄`E%E%鑄E%%鑄`E%EQ%鑄E%Q%鑄`E%EI1%鑄ﱎE%I1%鑄`LL`LeLLQ)08挹JIeU)T)Q⦁LjLQMBALLUTđ如LLLKMKMKLLjjj)iL%Ljjj)iLLeօ MLKJՅIe M MLKT LMKL?~|xp`@MKwKKKMKwKKKfKKKKfKKKK`eeeeeeeeFL%NjGH*MMFTjGH*-M&M8内H h%%KMMLMM`;MMݭ]7h ((LU(LUh]<] U]]I03ē0䒰 $ OLzU O]}(]]}]]}h]]}](0LTLnT8婅]媅8]<] 8塅墅 FV(8埅堅塅墅ɀjHhjHjH(j]hi]h}]]h}]]` - &&&&&8壪夐柈` S MR?Ƶ /Wi /W S0` Wee`ee`uꕒu땓ꕖŕ0'4Ŕ,0Ŗ LOʆ0 Ŗ LOWʈWe愾We憘 WWWL*SW򥁅5i8ehXHxXh8e$8e`L@ Xȑ`q悪ģ늦`8eꅖe녗ꅒ녓션톙i8ʅ` ^ X X UPeje hM UNeƠi摤 襖膑8*IT oYT ^LW8 -]Z.]ZM]AZN]BZm][n][]j\]k\J8坅8hXZxXZ ƀ뤝K8hXDZxXEZƁ뤔$0eօ i!Ie JՕ!ĘѢ@B$8eWVLCZ L[ 3R@4RA?RB@RCLZB@B@B@ B@ B@ B@ B@ B@B@B@B@B@B@B@B@B@$ 柩某feģL-ZLa\LN\0jƑLa\L[E>E< E: E8 E6 E4 E2E0E.E,E*E(E&E$E"E $ IT栢L[Ƒ e\L0\5` Ll\EQ>%Q>>EQ<%Q<< EQ:%Q:: EQ8%Q88 EQ6%Q66 EQ4%Q44 EQ2%Q22EQ0%Q00EQ.%Q..EQ,%Q,,EQ*%Q**EQ(%Q((EQ&%Q&&EQ$%Q$$EQ"%Q""EQ %Q `s[f[Y[L[?[2[%[[ [ZZZZZZZZZZZzZuZpZkZfZaZ\ZWZRZMZHZCZ*\$\\\\ \\\[[[[[[[[ ]]]\\\\\\\\\\\x\l\A '^#^%^&^ L^ O`^^ FD^*`()*+ X :P ;OL[M @ȑ`#^`^^L@^^,^ C]`,^C]`^`F / /^>~00`?xxpp___``x``i``0_ȱ_ ra ^`(`_,_0____i _8__ jII0 9N***I_ ?Ra@Ra3Ra4Ra_#LeaIJ ________ a__M_ a__M_ a__M_ʤƆƆĄZL``_,_0_#5IJ a_ a_ a_ʤĄT`aITȍa(`x__0 Ο_,_0 ^`(`x ra_(`x raΟ_(`,bn bbb_ݠ_0 ra___ T`,u0 fb,u_n hp` b,_0u__8___ __*_שׁ_ _ _,_0_```Lg^,u0,_0Huhull_hbb^^^ggbb d ,dggggg/e7eʎgygșg__,bp __b t,bL@b) bL@bbb ,bbbȭb,b ,b @dH,bX  bh ] ` sg d #e @Ee @5eLdfbb  bb`L@b  L@b` b b,b,b d d AdbH(b` dd`dd`dd`dd`L@d d d d(`ldd d d d(`ld bdd^dN^` a^ddd^#LP^!e"e^ e @-e` /UUUU,b0__meneLi^L@_8,bx0 e g(ff e(,bX`x0" o gf(`0(L@,_ȹ_`,bL@8 dwb a)**e p b_ M_0),_0U,gnF)e,eee ee_e gefLdحffTf b f,bfTfUf`ffLg^fxff(`fɀiff`8`ffɀi`gfng`  0 $0|x|x|x|g|888  ?>889|~p~n<00~~n@~8x||p|||pG`ppg@N8|N<8~p`g||||`|\||`@8g`p``8p8@|N8gx@~p==8?89s9p~~008~~8g`Npp`8G`8@@NN|`p8~`\w@8p`p@8px|8@|Np88np`8~8=?;8?s|p|~<00xx8~xx~~gppl`8G`@`@NN@8~pp`g@p8@88p8@|N`88npp8~893 898>s@ppx|~p00pp|~pp|xx88``G`N`FNNNp8888`G8@8`@8p8@\N8`xx88|8??s88<8s@@ppxx|0``~xx``x`|p<~p~|`||||<`pp|p||p|x|x`x@`@@|8x|xxx8x@Nx|xxpx@`|px=?888psp`x088<<|\L00 ppx졗P3-PwqŢT`Z%1+K>!էԦΦlaBt@ƨ̨ۨqwkǤ+ȥ{ "',3=ENW`ir{ȜϜ֜ߜ !#%-L_v̝&,6 to enter solution.# )(Time Remaining Label Point Find Point Invalid Format Laser No. Web Control Points Second Point Slope Time Level completed Bonus Points: shots left * = Game OverWebBeamScoreExample Practice , Step , Solution - OKSpaceCancelPrintPress any key to continue. Filename: Pathname:Openo0@y0T4B`n CB8`sx`n x  H@:(hxxChxPlease enter your name.dL`Xh :pU @8Use arrows to select date.VLTod:p0 kpmxp:7  E1b2E3b45$Select options for Graphing Level 1. Find Point Label PointMixedTimer  4 :=W@gMWUgbWjgw7UGb1w@M.'You cannot enter more than 25 problems. Please enter problem. .'Please enter first solution. .(Please enter second solution. .-Please enter an intermediate step. .25.UNTITLED No prompt selected for this step.,an appropriate instruction below. .(Welcome to the Alge-Blaster Plus Editor!Please select a menu item.OKSpaceCancelPrintPress any key to continue.25 Filename: Pathname:Open0@0T4B`n B8`sx`n  x  H@(hxxhxEditor written by: Louis X. Savain and David D. ElyLapU @8MLI Error $ X̟t@ t'Please enter a number not to exceed 8A'NZg [Zg@ ^Save changes to file?g8[HU HU '5;FTcv}˫׫ګݫ more than increased by the sum of the total of plus less than decreased by diminished by the difference of minus the product of multiplied by times twice double triple the quotient of divided by + - * /  x y and a number = is ( ) M|QXLcmu |  File Activity Subject  Level  Help  About.... EQ1 New Student Record Keeping--------------- See Record Print Record Setup Editor | E Quit | Q |SORStart Start with Stop | S Sound ----------- Options | O Review Text| R &4CNYiz Integers Order of Op. Mono. & Poly. Factoring Equations Systems of Eq. Algebraic Frac. Radicals Quadratic Eq. Level 1 Level 2 Level 3 Level 4 Your File ? TH"/G8 Info | ? Terms | T Hints | H ------- Grid | G 5AqOS RQ&7J]jGw  IDU |  File Problem  Step About... New Open | O Save | S Close -------- ABP | R Quit | Q Next Prob | Prior Prob |  Insert Prob Delete Prob Goto Prob # | G Next Step |  Prior Step |  Insert Step | I Delete Step | D Undo | U AAN1 /RECORDS/ /NEWDATA/"=z'4AN[ Xw$8""~""8"d p`"D `C"d "D @s"d @"d"8 w 1)F0"hL  w " P"`H1 w `0`} `]``Y{\;p`] w @` x l~`x_~p+<`  w `LD0fl fD``L@MLI p Tw@"p"@\w@L`Lp`LL@ %w HxQK0@fh%w Hxw8w8w8ww%w H@pp8`$%w H @@@@@ Iw L!  ` D"@@ @@D@@H@@" @`B H @@@ B@@D@ 00<Iwh0 @@ @   @D" @@@H"@P B@D @   L$ B@BB #D$ @"@ $ A@"0 @ D@@(D  !H@0D!   @@  "  @@ D "@"B@ D D@@   "@ "@D@D @ @ D"$$@ @ @~w X+ H"D@@0 @  `0"@ @@@  B@@B"@  @!@@@!D@@@&@ "@@ 0@ D@DD@  D0@$@$   H!   @PFwBxx@px`<x@pxx<@p x<@@ @p`x<p`p<p@ `@@x@@x@>px?||`?x~@p~p``<x`xx~s~xp|ppaC<<@pxx`x<ap~xpAx`@x@xac~pxx`xx`xax>o~<<x~<|xpAg`qpxx@pyx`@pax`pAg<`@>@pwax<`p`@<```x`x@@`pp@x``p>@xx`?```x`@|``x|??@~xxxp`x``>px`pA@`x`p```ppx<`x`p``p<xx<@``xp|p~x>xxx`>@xpp`?<<@`ppx|~x<x<@|x>xxpaC?px|"Dp`?<>`xx`|~?~?`C<@|x>xx`c>@x<?p@x<<`<|p`x>xxp@gx`xx>p?px@gx`x<@`p<`<<``xpAppq>x>p?px`p@ڢpppA<`<<``~pA`@pxx~x`@pAxpx<@>@<|ppxxx<@g@?ppxxx|x`TO``||?<x`~~?~?~`C|`xxxx`?`?@@T`|`||<`?`|gx<x|@@xppp@?p~@``x@<@`p@<`*Erx<@S.OwIp@?`pxp@?`pxp@<`px@0p@<`px@p@x<`px@@<p`?@x<@`?`@`>p<pAp|x<@z@p<@xpAx<`xpa<p?p>xpax<x@`p<``Cx<p`cx@?p?<@<<x@?@p`|?pAx<~pa@?`?p<`@|x@xp<~x@`xa@piB!8  8  L i LQ                                                          HH`=Xj~Ы߫ 2XcѬOdέ2wͮݮ'/6^m~ůܯ?t˰jPвC.Xpϴ /C-01`a !` LL.0` `PȌ0`89  L:; `:; L:; Ȍ` >6 4M0L4M0iL4M0i`,L L,LL, LL,L쫩m::m;;L,L쫩 L쫵 NiOi,0`L ii,0`L,L L3,,0`L,0`L*8L*8L*8 L:m>ʕ;m?L8:;L`0` k&*<:@;A6  LȌȈPQH2h HhPȌ0i0L k:B;C6L(*<@:A;6  L k$*<:D;E8DBEC B:C;6  L k,*8 <:F;G4  L k:H;IL*Ȍ<F:G;4  L k,*<:J;K8JHKI H:I;4  L k,Ȍ0*8 < 0`L k,0*<  L LLuuu u ` ޮȹLu u LLLLMȹLLWLLLȹLLL ޮL ޮLʈ Lyy  L ޮȹLuuLȭ:;LȹPO080Lȹ0/`_ L L23LʩLʕՍ8Lé L L i&i"i $i*i(#%')+!LijL"iiijijiNjO@ݠijLTiiijijij@LKLMNilimqriviwiiiii;i<i GiHi AiBi LiMiii !i"i ii &i'L Y d,KLL|MN @& @ @%L0123456789abcdxyz()+-={}*/.,?_ 0L$*<%+=@ABC67230145./,-8:9;Lz{jwkxȹ) Ldz᳍ ȳⳍ ޳߳.YLƳ-+ȹ+ȹ,ȹ,.,ɀ ++LƳLP)i80LLP)o oPL)   LLȹȘLP) LL;ȹP) LL) LҴLLLLL LHhx 0 LXeLlXLx ) LXȹ) 蹀Lȹ mBȹP􊦈mBBW8 L V u> uLLΪ0ΨΩ`X-H Ȅ UIJ  PZUIJ  % 0>T֤ Ȅ  H h  hՍ8LõHUȄ Ȅ    ȩU 0սIJ ՍTܭi 0Ai 0ձ v v0ݥʩʥLva{?/`Ս8Lõـ ̀LvLv                                                                                                                                                                                                                                                                           Solve. Factor. Reduce. Simplify. Find the sum. Find the difference. Find the product. Find the quotient. Find the solution set. Subtract smaller absolute value from larger. Determine sign. To subtract a number, add its opposite. Determine sign and add. Determine sign and subtract. Determine sign and multiply. Determine sign and divide. Express meaning of exponent(s). Evaluate inside parentheses. Evaluate using exponent(s). Multiply or divide from left to right. Add or subtract from left to right. Group coefficients of like terms. Combine coefficients. Distribute negative sign. Regroup coefficients and variables. Multiply where indicated. Multiply coefficients and add exponents of like terms. Raise monomials to indicated powers. Raise coefficients and variables to indicated powers. Use Distributive Property of Multiplication. Use Addition Property of Equations. Use Multiplication Property of Equations. Use the FOIL method. Combine like terms. Use APOE to collect variables on one side. Factor out the GCF. Find a,b so a*b = constant, a+b = linear coefficient. Determine separation of linear term. Factor GCF out of each binomial. Add equations. Determine remaining variable by substitution. Multiply equation(s) by a constant. Substitute variable expressions. Use APOE to isolate a variable. Rewrite equation to isolate variable. To divide, subtract exponents. Multiply numerators, multiply denominators. Combine fractions with common denominators. Multiply by factors needed to create LCD. Raise each fraction to higher terms. Multiply both sides of the equation by LCD. Factor as a difference of squares. Factor the radicand using a perfect square. Write as a single radical. Rationalize the denominator. Combine like radicals. Set each factor equal to zero and solve. Write in standard quadratic form. Identify coefficients a, b, and c. Use quadratic formula to solve. Write ordered pair. Change division to multiplication by reciprocal. Write in simplest radical form. Reduce coefficients. Determine LCD. Take square root of perfect squares. Rewrite as a product of two binomial factors. Simplify and write as a solution set. Find square root of first and third terms. Simplify by cancelling common factors. Factor and gather together as one fraction. Factor using general trinomial method. Evaluate numerator and denominator. Rewrite as a product of GCF and binomial factors. <!0/Jjpv> u  q  u  E % 1 N iWs}C9/ ^=IV`|{sf%e[N'8QSYf3l ; !c!Absolute valueAddition Prop. of Eq. (APOE)Additive inverse Assoc. Prop. of Addition Assoc. Prop. of Multiplication Axes Base Binomial Coefficient Commutative Prop. of Add. Commutative Prop. of Mult. Consecutive integers Constant Coordinate Denominator Difference Difference of two squares Diminished Distributive Prop. of Mult. Division Property of Eq. Equation Exponent Expression Factoring Factors FOIL method Greatest Common Factor (GCF) Improper fraction Integer Inverse Inverse operation Least Common Denominator (LCD) Least Common Multiple (LCM) Like terms Linear term Monomial Mult. Prop. of Eq. (MPOE) Multiplicative inverse Numerator Ordered pair Perfect square Polynomial Power Product Quadratic equation Quadratic formulaQuotient RadicalRadicand Reciprocals Slope of a line Slope-intercept formula Square Square root Standard form of an equation Subtraction Prop. of Eq. Sum System of equations Trinomial Variable The value of a number without regard for its sign. The absolute value of -9 is 9. Any real number can be added to both sides of an equation without making the equation an inequality. For example, if 6x + 4 = 10, then 6x + 4 + 2 = 10 + 2. The additive inverse of a number x is -x. The sum of a number and its additive inverse is 0. (7) + (-7) = 0 When adding, we can change the grouping of the addends. For all real numbers x, y, and z: (x + y) + z = x + (y + z). When multiplying, we can change the grouping of the factors. For all real numbers x, y, and z: (xy)(z) = (x)(yz). Plural for axis. A reference line, such as the horizontal or vertical axis in a coordinate plane. For example, the x-axis and the y-axis on a graph. In the example 3^2, 3 is the base that is to be multiplied by itself the number of times indicated by the exponent. 3^2 = 3*3 A polynomial with two terms. 5a + 6 and 7x^2 - 3z^2 are binomials. A coefficient is the multiplier of a variable. In 4x - 3y, 4 is the coefficient of x, and -3 is the coefficient of y. When adding, we can change the order of the addends without changing the value. For all x and y: x + y = y + x.When multiplying, we can change the order of the factors. For all x and y: x * y = y * x. Whole numbers that follow each other from the smallest to the largest, (x, x+1, x+2, x+3...). If x = -5, then the next consecutive integer would be -4.The constant term in an equation always represents the same value. In the equation 7b^2 + 3b + 2 = 0, 2 is the constant term. The number associated with a point on a number line. Also a point on a graph represented by an ordered pair of numbers. The number or expression below the fraction bar is the denominator. In the fraction 9/11c, 11c is the denominator. The difference is the result of subtraction. In 10 - 4 = 6, 6 is the difference. An expression of the form a^2 - b^2, which can be factored to (a + b)(a - b). If a = 5 and b = 7, then 5^2 - 7^2 = (5 + 7)(5 - 7). 5 diminished by 3 means 5 decreased by 3, which is 5 - 3, or 2. The product of a term and a polynomial can be written as the sum of several products. For all real numbers x, y, and z, x(y + z) = xy + xz, and xy + xz = x(y + z). Both sides of an equation can be divided by any real number not equal to zero without making the equation an inequality. If 6x = 7, then 6x/6 = 7/6. A mathematical sentence that uses the symbol of equality. 9x - 3 = 15 is an equation. The small raised number which indicates how many times the base is multiplied by itself. In the example 5^4, 4 is the exponent. The expression is an equivalent, but shorter, way of writing 5 * 5 * 5 * 5. Any group of terms connected by operation signs. 8x - 2 is an expression. The process of separating the factors of a product. For example, 12 could be factored as 12*1, 6*2, or 3*4. Any numbers or variables multiplied to form a product. In the equation 3x(12) = 36x, 3x and 12 are factors of 36x.The method for multiplying binomial terms. For example: (2x + 3)(x - 4) First: (2x)(x) = 2x^2 Outer: (2x)(-4) = -8x Inner: (3)(x) = 3x Last: (3)(-4) = -12 Then add and simplify, 2x^2 - 5x - 12. The largest monomial term that is a factor of all numbers and variables in a list of terms. For example, the GCF of 6b^4c^2 and 2b^2c^3 is 2b^2c^2. The GCF of 32 and 48 is 16. A fraction whose numerator is equal to or greater than its denominator. A member of the set of positive and negative whole numbers, including 0. {...-3, -2, -1, 0, 1, 2, 3...} The opposite of a number or variable. 8 and -8 are inverses.An operation which reverses a corresponding operation. Addition and subtraction are inverse operations. Multiplication and division are also inverse operations. The least common multiple of the denominators. It is needed to add or subtract fractions that do not contain common denominators. The smallest positive whole number that is exactly divisible by two or more given whole numbers. The LCM of 4, 5, and 10 is 20.Terms which have the same variables. In like terms, corresponding variables have the same exponents. 9xy^4, (-13)xy^4, and 178xy^4 are like terms. 9xy^4, 9x^4y, and 9y^5 are not like terms. A first degree term in a polynomial. In 5x^3 - x + 17 = 89, -x is the linear term. A number, a variable, or the product of a combination of numbers and variables. 7, 9x, and 5b^3 are all monomials.Multiplying each side of an equation by the same nonzero number results in an equivalent equation. For all real numbers a, b, and c, if a = b, then ac = bc and ca = cb. If a = 5, b = 5, and c = 8, then (5)(8) = (5)(8) and (8)(5) = (8)(5).One number is the multiplicative inverse of another when their product equals 1. Also known as a reciprocal. For example, (1/5)(5) = 1. The number or expression above the fraction bar is the numerator. In 11c/50c, 11c is the numerator.A pair of numbers in which the order is important. Together, both numbers define the location of a single point. For example, (3, -2) defines a point in the fourth quadrant of a graph. A rational number whose square root is a whole number. For example, 64 is a perfect square. The square root of 64 is 8 or -8. Two or more monomial terms connected by an operator. 4c^2, 2b - 58, and 5x^3 + 4x - 17 are all polynomials. The power of a term is indicated by the exponent. The power of 4^2 is 2. The result of multiplication. For example, 5 * 6 = 30. The product of 5 and 6 is 30. The variable in any given term of a quadratic equation is raised to the second power, but no higher. For example, 4x^2 - 7x + 5 is a quadratic equation.The formula used to compute the solutions of a quadratic equation of the form ax^2 + bx + c = 0.The result of division. For example, 48/6 = 8. 8 is the quotient.The symbol and the whole expression indicating that a root is to be taken.The expression or number under a radical sign. Two numbers whose product equals one. For example, 5/2 and 2/5 are reciprocals. Also called multiplicative inverses. The quotient of the vertical change (rise) between any two points on a given line and the horizontal change (run) between the same two points.If a line contains coordinate pairs (x1,y1), (x2,y2) and x1 does not equal x2, then the slope, m, equals y2-y1/x2-x1. The slope of a horizontal line is 0 and a vertical line has no slope. The square of a number is the product of the number and itself. The square of 5, also written as 5^2, is 5*5 or 25. A number which when multiplied by itself yields the given number. The square root of 49 is 7 or -7.ax^2 + bx + c = 0 is the standard form of an equation. Any real number can be subtracted from both sides of an equation without making the equation an inequality. If 6y + 4 = 9 then 6y + 4 - 4 = 9 - 4. The result of addition. In 2 + 3 = 5, the sum is 5. A set of linear equations containing the same variables. A solution to a system of equations satisfies all equations in the set. 3x - 4y = 12 and 2x + 3y = 25 is a system of equations. {8, 3} is the solution set. A polynomial made up of three monomials. 2x^3 + x^2 - b is a trinomial.A letter used to represent an unknown value. In the equation 7b + 9 = 23, b is the variable. (Օ"""*" """"ՁЁ ՅЀ  iեե i i } Օq  p p q t{Ą} ՀՀzՁՁ~  ~ ~  ~ Օ ~ ՕՅЅՕՅՁ ՕՅЀ  ՁՕ   ՅՀ } Ԁ|  Օ   ՕՀ  ~ՁԔ ~  ՁՕЁ  ՕՁԁ  Յ  ՕՔڪՕՕՅ յ~Չ ƄĄƦqՕrՀՀ ~  եՔ ĤՍȕ յҥ ĤĤ ȕ  յ ժĪ"ܕ#$*?(055+--++++ " ՀԀ! 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LmL  SubMe 5  doMen"OLԟ+  domen1 M JDL_ : DVenN L BUpVene } PassKesOLLLLL KVen JDLv V O 0 L PassIO}m the+looŠ M jV v V O 5 JDLW0 Π _ LO  G O  G v]UY4ZHOqJOeJOuHOZJO}JOC^GOv}x ƛGO &'()*+,-./0123456789E~Rd_Buf~ v5 w$ e y DLV  M 09fMO 0m_ O  GEDstoVaE~ wM M  _ mp   _  myDelet~ ``ZLwO aa0 ``mZLwO aa addCo~ `LO `` ZLwO 0 wa addSpac ``ZLwLO a myLEP3 V O ~0 09fMO >a 0 a GEDtesT w O 8Cx w O "Cx  w  qO w 0 w  EDPars w vw O~V wO 5 O~ M O~V wO 5 O~0 w V wO 5 O~ _ >  flushGE yM EDmod7 v]UY EDiniN BkbW)a GEDInia v 2vykj GEDValiv 09fMM --fMM V  M V M V M V _ _ _ _ _  GEDerro qx  GEDbac v]UYal}V GEDch 5 wO "0 qx  GE> O V  O v~G0 ]v XCentecJYCenteJZVertAxi |Z$ m$ 3mDV S}$ m$ = DV S}V <mw $ $ <mDV< jV|v w  M p w p DV_ jVp  MinusSig L M$  $ DVjV XLablePoF v  9 mDV S}p DVS} XLableNep v  9mmR DV S}p  YLablePo v   9m DV S}p aDVS} YLableNe v   9 mR DV S}p  HorzAxiZ |Z$ mM p $  DVS}$  $  DVS}p w _ $ DV MjV|v w  M p w p \DV_ XjVp  GrafBo Y|hVY|xxxx}VY MakeGrafB5 v]U? 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L# O  SecPCm# v! Lyv P5vO O ^yvO O L@v P. O 6v O > > v PLyv O. O v0 v(}L iSecPEd v  iSlopE Evyrjv  GetNu E 2ndGe2 V  O  M0 ; BigParsG G vyGNvvGV  -O ; 0 ;M v(}V  -O P 0 PM L_ _ >  SecPParsn v RoteۛOl G ChkSPn 3x  m6x  m LnO "LyvP5vO  M  MvP0 Lv SecPE V O 0 <V  O 0 *V  O 0 V O 0 vO uL$5 v0 2V  O 0 V  O 0 vO 5 v SlopEDY $ / O V   O a0 5 yv $  Study the given point and slope. $12 Study the given points. $^ !Use the arrows or mouse to select $2ႝ point 2 . $ !Enter the correct slope . $4͝   $ &To change options during the activity, $  press | O. $: Calculate the slope using the $P slope-intercept formula. 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The / will be provided for you. $} To block an asteroid: $ $ Press to select Web Control. $ˣ " Enter the first coordinate pair. $ , Enter the second coordinate pair . 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The absolute value of a number is the distance between the number and 0 on a number line. The absolute value of 3 is 3. The absolute value of -3 is also 3. ^2 If the signs are mixed, first add together the numbers with the same signs. ^3 Then, subtract the smaller absolute value from the larger. Remember to disregard the signs. ^4 The final answer takes the sign of the number with the larger absolute value. ~ @22 Subtracting Integers %3 ^1 Subtraction is the same as adding the inverse (opposite) of the second number. ^2 To add the inverse, rewrite the problem as addition and change the sign of the second number. ^3 Add the numbers. ~ %4 ^1 Subtraction is the same as adding the inverse (opposite) of the second number. ^2 To add the inverse, rewrite the problem as addition and change the sign of the second number. ^3 Then subtract the smaller absolute value from the larger. Remember to disregard the signs. ^4 The final answer takes the sign of the larger number. ~ @32 Multiplying and Dividing Integers %2 ^1 If there are an even number of negative terms (or if there are none), the answer is positive. ^2 Determine the sign and multiply or divide as indicated. ~ %2 ^1 If there are an odd number of negative terms, the answer is negative. ^2 Determine the sign and multiply or divide as indicated. ~ 3 @12 Order (Integers) %3 ^1 If there is more than one operation to perform, follow the rules for Order of Operations. ^2 First, multiply and divide, working from left to right. ^3 Second, add and subtract, working from left to right. ~ %3 ^1 If there is more than one operation to perform, follow the rules for Order of Operations. ^2 First, multiply and divide, working from left to right. ^3 Second, add and subtract, working from left to right. ~ @22 Order (Exponents) %4 ^1 The exponent indicates how many times the base is used as a factor. ^2 First, evaluate terms with exponents. ^3 Second, multiply and divide, working from left to right. ^4 Third, add and subtract, working from left to right. ~ %4 ^1 The exponent indicates how many times the base is used as a factor. ^2 First, evaluate terms with exponents. ^3 Second, multiply and divide, working from left to right. ^4 Third, add and subtract, working from left to right. ~ @32 Order (Grouping) %4 ^1 When an equation includes exponents and grouping symbols such as parentheses and fraction bars, the rules for Order of Operations are slightly different. ^2 Operations within parentheses must be performed first. ^3 Next, evaluate terms with exponents. ^4 Multiply and divide (left to right); then add and subtract (left to right). ~ %4 ^1 When an equation includes exponents and grouping symbols such as parentheses and fraction bars, the rules for Order of Operations are slightly different. ^2 Evaluate the numerator and the denominator first (exponents, multiplication and division, addition and subtraction). ^3 Multiply and divide from left to right. ^4 Add and subtract from left to right. ~ 3 @12 Adding and Subtracting Like Terms %2 ^1 Like terms have identical variables and exponents. ^2 Add the coefficients of like terms. ~ %2 ^1 Like terms have identical variables and exponents. ^2 Subtract the coefficients of like terms. ~ @22 Multiplying Monomials %3 ^1 Multiplication is commutative (the order doesn't matter). ^2 Group coefficients and similar variables together. ^3 Simplify by multiplying coefficients and adding the exponents of like variables. ~ %4 ^1 When a monomial term in parentheses is raised to a power, raise each part of the monomial to the power indicated. ^2 Raise monomials to indicated powers. ^3 To raise variables with exponents to a power, multiply the two exponents. Simplify non-variable terms with exponents as usual. ^4 Simplify by multiplying coefficients and adding the exponents of like variables. ~ @32 Multiplying Polynomials %3 ^1 By using the Distributive Property, the product of a monomial and a polynomial can be written as a sum. ^2 Rewrite the multiplication expression as a sum, multiplying each term of the polynomial by the monomial outside the parentheses. ^3 Simplify each product. ~ %4 ^1 The FOIL (First, Outer, Inner, Last) method helps you multiply two binomials. ^2 Use the FOIL method. Multiply the First terms of each binomial, then the Outer terms, then the Inner terms, and finally the Last terms. Rewrite the expression as a sum. ^3 Find each product. ^4 Simplify and combine like terms. ~ 4 @12 Factoring out the GCF %3 ^1 To factor a polynomial, find its Greatest Common Factor (GCF). The GCF is the lowest term that is a factor of all numbers and variables in a problem. You must look at both the coefficients and the variables. ^2 First, factor out the largest common factor of the coefficients. ^3 Then factor out the lowest power of the common variables. Write the common factors of the coefficients and variables as a product outside the parentheses. ~ %3 ^1 To factor a polynomial, find its Greatest Common Factor (GCF). The GCF is the lowest term that is a factor of all numbers and variables in a problem. You must look at both the coefficients and the variables. ^2 First, factor out the largest common factor of the coefficients. ^3 Then factor out the lowest power of the common variables. Write the common factors of the coefficients and variables as a product outside the parentheses. ~ @22 Special Factorizations %4 ^1 If a polynomial represents the difference of two squares both terms will be perfect squares. ^2 First, find the square root of the first term. ^3 Find the square root of the second term (disregarding the negative sign). ^4 The first factor is the sum of the two roots. The second factor is the difference of the two roots. ~ %5 ^1 Learn to recognize a trinomial square. The first and third terms will be perfect squares. The middle term will be twice the product of the two square roots. ^2 First, find the square root of the first term. ^3 Find the square root of the third term. ^4 Check to see if the middle term (disregarding its sign) is twice the product of the two square roots. ^5 The sign of each term has the same sign as the middle term of the perfect square trinomial. ~ @32 Factoring Trinomials %4 ^1 If the term in which the variable is squared (the quadratic term) has a coefficient of 1, use the following method. ^2 First factor the quadratic term. ^3 Find two numbers whose product is the last term (the constant) and whose sum is the coefficient of the middle term (the linear term). ^4 Form two binomial factors, each containing a variable factor and a number factor. ~ %6 ^1 If the coefficient of the quadratic term is not 1, use the following method. ^2 Multiply the constant (the last term) by the coefficient of the quadratic term (the first term). ^3 Find the two factors of this product whose sum is the coefficient of the linear term (the middle term). ^4 Using these two numbers as coefficients, rewrite the single linear term as two terms. ^5 Factor out the GCF of the first two terms; then factor out the GCF of the second two terms. ^6 Use the common binomial in parentheses as the first binomial factor in the answer. Use the two terms outside the parentheses as the second binomial factor in the answer. ~ @42 Factoring Completely %3 ^1 Factor each polynomial completely, using one or more of the factoring methods you have learned. ^2 Always begin by factoring out any GCF (other than 1). ^3 If possible, factor the remaining polynomial as either the difference of two squares or a trinomial square. ~ %7 ^1 Factor each polynomial completely, using one or more of the factoring methods you have learned. ^2 Always begin by factoring out any GCF (other than 1). ^3 Factor the remaining trinomial. Multiply the constant (the last term) by the coefficient of the quadratic term (the first term). ^4 Find the two factors of this product whose sum is the coefficient of the linear term (the middle term). ^5 Using these two numbers as coefficients, rewrite the single linear term as two terms. ^6 Factor out the GCF of the first two terms; then factor out the GCF of the second two terms. ^7 The first factor in the final answer is the GCF of the original expression. Use the common binomial in parentheses as the second factor. Use the two terms outside the parentheses as the second binomial factor in the answer. ~ 3 @12 One Step Equations %3 ^1 According to the Addition Property of Equations, adding the same value to both sides of an equation results in an equivalent equation. ^2 Use the Addition Property of Equations to isolate the variable on one side of the equal sign. Add the inverse of the numerical term to both sides of the equation. ^3 Simplify. ~ %3 ^1 According to the Multiplication Property of Equations, multiplying both sides of an equation by the same nonzero number results in an equivalent equation. ^2 To remove the coefficient of a variable, use the Multiplication Property of Equations. (Multiply both sides of the equation by the reciprocal of the coefficient.) ^3 Simplify. ~ @22 Two Step Equations %5 ^1 In some equations, you will need to use both the Addition Property and the Multiplication Property. ^2 Start by using the Addition Property to isolate the variable term. (Add the inverse of the constant to both sides.) ^3 Simplify. ^4 Then use the Multiplication Property. (Multiply both sides by the reciprocal of the coefficient of the variable.) ^5 Simplify. ~ %5 ^1 In some equations, you will need to use both the Addition Property and the Multiplication Property. ^2 Start by using the Addition Property to isolate the variable term. (Add the inverse of the constant to both sides.) ^3 Simplify. ^4 If the variable's coefficient is -1 (or just a negative sign), multiply both sides of the equation by the reciprocal of -1, which is -1. ^5 Simplify. ~ @32 Equations with More Steps %7 ^1 If an equation includes a polynomial multiplied by a monomial, first use the Distributive Property to simplify. Then use the Addition Property and the Multiplication Property as necessary. ^2 Use the Distributive Property. ^3 Simplify by collecting like terms. ^4 Use the Addition Property to isolate the variable term. ^5 Simplify. ^6 Use the Multiplication Property to find the value of the variable. ^7 Simplify. Reduce any fraction, but leave it in improper form. ~ %8 ^1 If an equation includes a polynomial multiplied by a monomial, first use the Distributive Property to simplify. Then use the Addition Property and the Multiplication Property as necessary. ^2 Use the Distributive Property. ^3 Use the Addition Property to get all variable terms on one side of the equation. (Add the opposite of the smaller variable term to both sides.) ^4 Simplify by collecting like terms. ^5 Use the Addition Property again to isolate the variable. ^6 Simplify. ^7 Use the Multiplication Property to find the final answer. ^8 Simplify. Reduce any fraction, but leave it in improper form. ~ 2 @12 Solving by Elimination %7 ^1 Two or more equations with the same variables form a system of linear equations. To solve such a system, find the ordered pair that makes both equations true. ^2 Add all the members of the first equation to those of the second. One variable is cancelled out so that a simple equation with only one variable remains. ^3 Use the Multiplication Property to find the value of the variable. ^4 Substitute the value of this variable into the simpler of the two original equations. Find the value of the remaining variable. ^5 Use the Addition Property to isolate the variable term and simplify. ^6 Use the Multiplication Property to find the value of the remaining variable and simplify. ^7 Write the two values as an ordered pair (in alphabetical order). ~ %9 ^1 Two or more equations with the same variables form a system of linear equations. To solve such a system, find the ordered pair that makes both equations true. ^2 In some equations, the coefficients of one variable do not cancel out. In this case, use the Multiplication Property to multiply equation(s) by a number(s) that will cause the coefficients to cancel. ^3 Simplify. ^4 Add the members of the first equation to those of the second, cancelling out one variable. ^5 A simple equation with only one variable remains. Use the Multiplication Property to find its value. ^6 Substitute the value of this variable into the simpler of the two original equations. Find the value of the remaining variable and simplify. ^7 Use the Addition Property to isolate the variable term and simplify. ^8 Use the Multiplication Property to find the value of the remaining variable and simplify. ^9 Write the two values as an ordered pair (in alphabetical order). ~ @22 Solving by Substitution %8 ^1 The substitution method is another way to solve a system of linear equations. ^2 If a variable in one equation is isolated on one side of the equal sign, substitute the value of that variable into the other equation. ^3 Multiply. ^4 Collect like terms. ^5 Use the Multiplication Property and/or Addition Property to find the value of the variable. ^6 Substitute the value of this variable into the simpler of the two original equations to find the value of the remaining variable. ^7 Simplify. ^8 Write the two values as an ordered pair. ~ %10 ^1 The substitution method is another way to solve a system of linear equations. ^2 Select the simplest equation and use the Addition and/or Multiplication Property to isolate the single variable term. ^3 Substitute the value of this variable into the other equation. ^4 Distribute. ^5 Collect like terms. ^6 Use the Addition Property to isolate the variable and simplify. ^7 Use the Multiplication Property to find the value of the variable and simplify. ^8 Substitute the value of this variable into the simpler of the original equations to find the value of the remaining variable. ^9 Simplify completely using the Addition and/or Multiplication Property. ^10 Write the two values as an ordered pair. ~ 4 @12 Simplifying %3 ^1 Algebraic fractions can be reduced only if a factor of the numerator also occurs as a factor of the denominator. ^2 When reducing a fraction with two monomials, first reduce the numerical coefficient factors. ^3 Next, reduce the variable factors. If similar variables have exponents, subtract the smaller exponent from the larger. Put the result where the larger exponent was and simplify. ~ %3 ^1 The quotient of two polynomials is one type of algebraic fraction. Factor before dividing. ^2 First, factor the numerator, then the denominator. ^3 Cancel any factor which appears in both the numerator and the denominator and simplify. ~ @22 Multiplying and Dividing %3 ^1 When an algebraic fraction contains polynomials, factor before dividing or multiplying. ^2 First factor the polynomials. Write as a single fraction. ^3 Cancel any factor which appears in both the numerator and denominator. Simplify. ~ %4 ^1 Dividing by an algebraic fraction is the same as multiplying by the reciprocal of that fraction. ^2 Rewrite the problem as multiplication. ^3 First factor the polynomials. Write as a single fraction. ^4 Cancel any factor which appears in both the numerator and the denominator. Simplify. ~ @32 Adding and Subtracting %3 ^1 Fractions must have common denominators in order to be added or subtracted. ^2 Add or subtract the numerators. ^3 Reduce the result whenever possible. ~ %7 ^1 Fractions must have common denominators in order to be added or subtracted. ^2 First, factor each binomial denominator. ^3 Determine the lowest common denominator (LCD). Write the LCD as a product containing each different factor found in the denominators. ^4 Multiply the numerator and denominator of each fraction by the factor needed to create the LCD. ^5 Simplify. ^6 Combine the numerators, now that they have common denominators. ^7 Reduce the result if possible, and simplify. ~ @42 Solving Fractional Equations %5 ^1 One method of solving a fractional equation is to eliminate the denominators. ^2 First, find the LCD of the fractions. ^3 Multiply each term of the equation by the LCD. ^4 Simplify and eliminate all denominators. ^5 Solve the resulting equation. ~ %5 ^1 A fractional equation can be solved most easily by first using the Multiplication Property to eliminate the denominators. ^2 First, find the LCD of the fractions. ^3 Multiply each term of the equation by the LCD. ^4 Simplify and eliminate all denominators. ^5 Solve the resulting equation using the steps you have learned. ~ 3 @12 Simplifying %3 ^1 The square root of a number is one of its two equal factors. The principal square root is a positive number. The principal square root of 36 is 6. ^2 To simplify a square root, factor the radicand (the number inside the radical). Use a perfect square (4, 9, 16, 25, ...) for one of the factors. ^3 Remove the perfect square factor by writing its principal square root in front of the radical sign. ~ %5 ^1 Every positive real number has two square roots, one positive and one negative. The square root of 49 is +7 or -7. ^2 To simplify a square root that involves variables, first factor the numerical coefficient using a perfect square. ^3 If the exponent is odd, separate the power into two factors. Use the largest possible even exponent as one factor. ^4 Then remove the perfect square numerical factor by writing its square root in front of the radical. ^5 Finally, take the square root of the even powers. (Divide the exponents by 2.) ~ @22 Multiplying and Dividing %5 ^1 When multiplying radical expressions, multiply the coefficients and the radicands separately. ^2 First, multiply the coefficients; then, multiply the radicands. ^3 Factor the radicand using a perfect square. ^4 Remove the perfect square factor by writing its square root in front of the radical. ^5 Simplify. ~ %3 ^1 A radical expression in simplest form cannot have a radical in the denominator. ^2 To "rationalize the denominator," multiply both terms of the fraction by the radical in the denominator. ^3 Simplify, noting that any radical times itself (squared) equals the radicand. ~ @32 Adding and Subtracting %2 ^1 Radical expressions may be added and subtracted only if their radicands are alike. ^2 Combine the coefficients of like radicands as one term. ~ %3 ^1 Radical expressions may be added and subtracted only if their radicands are alike. ^2 Simplify all radical expressions by taking the square root of perfect square factors. ^3 Combine the coefficients of like radicands as one term. ~ 2 @12 Solving by Factoring %5 ^1 A quadratic equation is written in standard form if the polynomial is equal to 0 and all terms are in descending order according to their exponents. ^2 Verify that the equation is in standard form; then factor the polynomial. ^3 Set each factor equal to 0. ^4 Solve the resulting equations. ^5 Write as a solution set. ~ %6 ^1 A quadratic equation is written in standard form if the polynomial is equal to 0 and all terms are in descending order according to their exponents. ^2 Rewrite the equation in standard form. ^3 Factor the polynomial. ^4 Set each factor equal to 0. ^5 Solve the resulting equations. ^6 Write as a solution set. ~ @22 Using the Quadratic Formula %7 ^1 Quadratic equations which cannot be factored can be solved by using the Quadratic Formula. ^2 Determine the value of the coefficients "a" and "b" and the constant "c." ^3 Substitute these values in the formula. ^4 Multiply. ^5 Simplify the radicand. ^6 Rewrite in simplest radical form. ^7 Reduce if possible. ~ %10 ^1 Quadratic equations which cannot be factored can be solved by using the Quadratic Formula. ^2 Rewrite the equation in standard form. ^3 Determine the value of the coefficients "a" and "b" and the constant "c." ^4 Substitute these values in the formula. ^5 Multiply. ^6 Simplify the radicand. ^7 Take square roots of perfect squares. ^8 Rewrite as two separate expressions, one with a plus sign and one with a minus sign. ^9 Simplify each numerator. ^10 Reduce if possible and write as a solution set. ~          !                  !          !            !                                        !                                              !     !          !         !              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