+JJJJ  X/ lӠˠӠϠӠϠԮԠҠˠčӠ٠ϠԮz=218z=8z=-3(y+2)(2y+1)=6y+5y=32y=-1x2-10x+25=4(x-2)x=3x=11(x-2)(3x-1)=100x=7x=-143(z+3)(z-3)=2z-1z=4z=-23y-25=8yy=4y=-1031=6m-9m2m=13(y-5)2-1=0y=y=62x2-x-10=2(x+5)x=4x=-52z2=14+5zz=-7x2=1x=1x=-14y2=1y=12y=-12x2-64=0x=8x=-8x2+x-20=0x=-5x=4y2-3y-18=0y=6y=-32x2-5x-3=0x=3x=-126z2+5z+1=0z=-12z=-1x2-3x+8=6x=x=22y2=7y+4y=4y=-12n(6n-5)=4n=43n=-12(z+1)(z-6)=ݙ3pD.oD2TORING EQUATIONS wt!!%Os KӜӜӜHTlӜӜ\fkl@nx,T@20/CYp ,Ii=-8b=-45(x+2)+4(x-4)+6=45x=51-25(10-x)=1x=103(x-4)+(4-x)2=16x=2038a+14a=25a=403=23(m+9)-1m=-3t11x=231x=21 x10=13x=130.6=n5n=33m+7=31m=842=35yy=701.6y=32y=20-63=3+6rr=-1151=z4+11z=1604y-y=-15y=-512-3x-2x=-3x=30=125-17x-8xx=542=3n+5n-nn=63(n-1)+4=-2n=-1(m+1)+(m+2)=41m=199b-(6b-4).cret.swit.shlx.asrx.psh.lpsh.pop.lpop.mulx.divx.modx.cpystk2.calip4՞۞םn4sn4om4 sYbbsh65.libelnm.26 c<20 &5CTct $;Skisspace__Top_settop_.fstswt.mul.div.udv.mod.umd.move.shl.asr.shr.cpystk.modstk.csav     y2(9x-y)(2x+2y)n5-16nn(n2+4)(n2)(n+2)m2n3+2m2-n3-2(m1)(m-1)(n3+2)12a4+21a2-63(2a1)(2a-1)(a2+2)9x4+8x2-1(3x1)(3x-1)(x2+1)+)(ab+3)18x3y2-27x2y39x2y2(2x-3y)18ab2-36a2b+18a318a(b-a)2-16x2y-10x2yz-x2yz2-x2y(+z)(8+z)-4m3+10m2+6m-2m(2m+1)(m-3)9b4-18b3c+9b2c29b2(b-c)2-27mn-42m-3mn2-3m(n+)(n+2)16xy+18x2-2ty3-9yy(y3)(y-3)-3m2+30m-75-3(m-5)2a3-ab2a(ab)(a-b)5x2-5x-1005(x-5)(x+4)3a2-27b23(a3b)(a-3b)18y3-60y2+50y2y(3y-5)275k2-147m23(5k7m)(5k-7m)9m2+6m-27m3-3m(3m2)(3m+1)4a2b2+20ab+244(ab.cret.swit.shlx.asrx.psh.lpsh.pop.lpop.mulx.divx.modx.cpystk2.calip4՞۞םn4sn4om4 sYbbsh65.libelnm.26 c<20 5Ni 4Y4___closallexit__exit_isdigit_isspace__Top_settop_.fstswt.mul.div.udv.mod.umd.move.shl.asr.shr.cpystk.modstk.csav4x2-9y2@(4x2)=2x @(9y2)=3yFactor 1=(2x+3y)Factor 2=(2x-3y)(2x+3y)(2x-3y)16x4-144y6@(16x4)=4x2@(144y6)=12y3Factor 1=(4x2+12y3)Factor 2=(4x2-12y3)(4x2+12y3)(4x2-12y3)[Z8`l6Lş_Ȍb_Ͳ] )Y h( ֭  D\D2E  D\D2C_SQUARESeKt^editP\ ڧ[eXP\ ڧ[ڧڧzڧڧSH<[H2ў`HH\`\Z[YS6`LxQɿu3'RͲʎRʎ]]]ɍuL͟ɍ}RLRɍg^H8 ^hZLɍR LͲɊRR% QLܤͲ Z@ -^ ş\[Z QY\ (-3)+(-7)+4(-3)+(-7)=-10 4=410-4=6(-3)+(-7)+4=-6-3+8+(-11)+28+2=10 -3+(-11)=-1414-10=4-3+8+(-11)+2=-4 ş\[Z QY\[Z8`l6Lş_Ȍb_Ͳ] )Y h( ֭  D\D2GNED_ADDITION3zt^editE eKt^editP\ ڧ[ڧڧzڧڧSH<[H2<x \ZLl8 ўR HH\`\Z[YS6`LxQɿu3'RͲʎRʎ]]]ɍuL͟ɍ}RLRɍg^H8 ^hZLɍR LͲɊRR% QLܤͲ Z@ -^   10[?]1TxQɿu3'RͲʎRʎ]]]ɍuL͟ɍ}RLRɍg^H8 ^hZLɍR LͲɊRR% QLܤͲ Z@ -^ ş\[Z QY\[Z8`l6Lş_Ȍb-15+(-21)+16-20-15+(-21)=-3636-16=20-2025+(-75)+625+(-50)52525+625=650-75+(-50)=-125650-1255256.1+(-7.01)+(-9.9)-10.81(-7.01)+(-9.9)=-16.9116.91-6.1=10.81-10.818+(-9)-19-8=1-1-5+727-5211+(-15)-415-11=4-471+(-52)1971-52191116+(-1512)-4131536-1116=413-4136+(-5)+(-11)-10-5+(-11)=-1616-6=10-10-9+13+(-10)+71-9+(-10)=-1913+7=2020-191lting equation tofind the value of the firstvariable. &Find the second variable bysubstituting the value found inSTEP 3 in one of the originalequations, and solve.^A&Rewrite one of the equations sothat one variable is expressed interms of the other. (One variablestands alone on one side of theequation.)&Use the expression found in STEP 1as a substitute for its variablein the second equation.&Solve the resut t t@ t tA t@nmtlinearsubstitution(97IM(N;(N8@>P\ ڧ[ڧڧ^j]ڧr|SWI bBBH b11W ԧ H h@ [_ /QSIRb_L`LLLL`ª`LQLYLeLXLeLee ўQH\(h0L& Ꝥ$`( R \ZLl8 ўR HH\`\Z[YS6` ^A&Rewrite the equation so the rightside equals 0.&Factor the left side completely(see procedures on factoring).&Set each factor equal to 0, andsolve each equation.&Check the solution. t t@ t tGrftfirstfactorBBN4(N19(N197BM MBFP\ ڧ[ڧڧeq]ڧySWI b  H b1wuW ԧ H h@ [_ /QSIRb_L`LLLL`ª`LQLYLeLXLeLee ўQH\(h0L& Ꝥ$`( R \ZLl8 ўR HH\`\Z[YS6ʉ    ş\[Z QY\[Z8`l6Lş_Ȍb_Ͳ] )Y h( ֭  D\D2DD SIGNEDTe3zt^editE eKt^editP\ ڧ[ڧڧzڧڧSH<[H10,G`1tўR HH\`\Z[YS6`LxQɿu3'RͲʎRʎ]]]ɍuL͟ɍ}RLRɍg^H8 ^hZLɍR LͲɊRR% QLܤͲ Z@ -^^A&Factor out the greatest commonfactor (GCF).&Find the binomial factors of theterms remaining in parentheses.( R \ZLl8 ўR HH\`\Z[YS6ʉ tAyltfacpolycompletely]]ɍuL͟ɍ}RLRɍP\ ڧ[ڧڧ_k]ڧs}SWI b$ H b1 tL@ kU8  L  Q^R(jQ0l^l\  wUuW ԧ H h@ [_ /QSIRb_L`LLLL`ª`LQLYLeLXLeLee ўQH\(h0L& Ꝥ$`2x+3=5+x2x-x+3=5+x-xx+3=5x+3-3=5-3x=2a+21=2a-10a-a+21=2a-a-1021=a-1021+10=a-10+10a=31\D2C_SQUARESeKt^e  DDD2  DDD2  D\D2RST_DEGREEڧ[@PP\ ڧ[@P\ ڧ[ڧڧzڧڧSH<[H2/eg^H8 ^hZLɍR LͲɊRR% QLܤͲ Z@ -^ ş\[Z QY\[Z8`l6Lş_Ȍb_Ͳ] )Y h( ֭  D\D2E  Dsto eliminate one variable.&Solve for the remaining variable inthe equation.&Find the other variable bysubstituting the value found inSTEP 3 in one of the originalequations.^A&Write both equations so that liketerms line up in the same columns.If needed, multiply each term inone or both equations by a constantso that the sum or difference ofthe two equations eliminates one ofthe variables.&Add or subtract the equation^A&Find the square root of each term.&The first factor is the sum of thetwo roots.&The second factor is the differenceof the two roots.&Write the two factors as a singleexpression. t t@ t tA tHsetfacsquaresB(97L9BM(N;CALP\ ڧ[ڧڧfr]ڧzSWI bBBH b1W ԧ H h@ [_ /QSIRb_L`LLLL`ª`LQLYLeLXLeLee ўQH\(h0L& Ꝥ$`( R \ZLl8 ўR HH\`\Z[YS6` t  ^A&Find the greatest common factor(GCF) of the polynomial.&Divide each term of the polynomialby the GCF.&Write the two factors as a singleterm.t t t@ t tA tKybtfacpolyB(97B((N197BM MBFF P\ ڧ[ڧڧiu]ڧ}SWI bBBH b1uW ԧ H h@ [_ /QSIRb_L`LLLL`ª`LQLYLeLXLeLee ўQH\(h0L& Ꝥ$`( R \ZLl8 ўR HH\`\Z[YS6` rite the result as one expression.&Rewrite the expression as theproduct of two binomials.P3 to rewrite the middle term of thetrinomial.&Rewrite the middle term as the sumof the factors found in STEP 2.&Using the four terms from STEP 3,factor the GCF from the first andsecond terms. Then factor the GCFfrom the third and fourth terms. W^A&Multiply the numerical coefficientof the first term by the last term.Be sure to consider the sign ofeach term.&Find the two factors of the product(from STEP 1) whose sum equals thecoefficient of the middle term.These factors will be used in STER \ZLl8 ўR HH\`\Z[YS6` tDsitfac2trinomialsfo"H.(N(N7?=HP\ ڧ[ڧڧbn]ڧvSWI bBBH b1\ kU8  L  Q^R(jQ0l^l\  wUuW ԧ H h@ [_ /QSIRb_L`LLLL`ª`LQLYLeLXLeLee ўQH\(h0L& Ꝥ$`( l8 ўR HH\`\Z[YS6` t tFbgtlinearaddsubAB(N(N086(N197BM MBFP\ ڧ[ڧڧdp]ڧxSWI b$ H b18  L  Q^R(jQ0l^l\  wUuW ԧ H h@ [_ /QSIRb_L`LLLL`ª`LQLYLeLXLeLee ўQH\(h0L& Ꝥ$`( R \ZL    ^A&Find the greatest common factor(GCF) of the numericalcoefficients.&Find the GCF of the literalcoefficients.&Write both GCF's as a singleexpression.[YS6` t t t@ tLfatfacgcfAN86(N3(N086AM MAEE P\ ڧ[ڧڧjv]ڧ~SWI bBBH b1R0l^l\  wUuW ԧ H h@ [_ /QSIRb_L`LLLL`ª`LQLYLeLXLeLee ўQH\(h0L& Ꝥ$`( R \ZLl8 ўR HH\`\Z^A&Using the Distributive Law,multiply each term of thepolynomial by the monomial.&Write the products obtained inSTEP 1 as a single expression.6` t t t@ t tFtgtpolymonomultBM(N4(N197BM MBFP\ ڧ[ڧڧdp]ڧxSWI bBBH b1l wUuW ԧ H h@ [_ /QSIRb_L`LLLL`ª`LQLYLeLXLeLee ўQH\(h0L& Ꝥ$`( R \ZLl8 ўR HH\`\Z[YS^A&Multiply the numericalcoefficients.&Multiply the literal coefficients.&Write the products (found above) asa single product.l8 ўR HH\`\Z[YS6` t t@nmtmonomultiplicationD(<:(N6(N3;9DP\ ڧ[ڧڧ^j]ڧr|SWI bBBH b1|  L  Q^R(jQ0l^l\  wUuW ԧ H h@ [_ /QSIRb_L`LLLL`ª`LQLYLeLXLeLee ўQH\(h0L& Ꝥ$`( R \ZL^A&Arrange terms in order.&Group like terms.&Add the inverse (opposite) of thenumber being subtracted.&Group and add like terms. HH\`\Z[YS6` t t tCnjtpolysubtractionA:(N6(N3(N086AM MAP\ ڧ[ڧڧam]ڧuSWI bBBH b1   Q^R(jQ0l^l\  wUuW ԧ H h@ [_ /QSIRb_L`LLLL`ª`LQLYLeLXLeLee ўQH\(h0L& Ꝥ$`( R \ZLl8 ўR   ^A&Add the inverse (opposite) of thenumber being subtracted.&Combine like terms by adding theirnumerical coefficients.Ll8 ўR HH\`\Z[YS6` t tCnjtmonosubtractionEG7(N4<:(N6><GP\ ڧ[ڧڧam]ڧuSWI bBBH b1@|  L  Q^R(jQ0l^l\  wUuW ԧ H h@ [_ /QSIRb_L`LLLL`ª`LQLYLeLXLeLee ўQH\(h0L& Ꝥ$`( R \Z^A&Arrange terms in the same order.&Group like terms.&Add like terms.l8 ўR HH\`\Z[YS6ʉ t tFngtpolyadditionEG(N4<:(N6><GMP\ ڧ[ڧڧdp]ڧxSWI b  H b1J  L  Q^R(jQ0l^l\  wUuW ԧ H h@ [_ /QSIRb_L`LLLL`ª`LQLYLeLXLeLee ўQH\(h0L& Ꝥ$`( R \ZL^A&Combine like terms by addingtheir numerical coefficients.ZLl8 ўR HH\`\Z[YS6` t tFngtmonoadditionBE(NN197(N4<:EM MP\ ڧ[ڧڧdp]ڧxSWI bBBH b1U@  L  Q^R(jQ0l^l\  wUuW ԧ H h@ [_ /QSIRb_L`LLLL`ª`LQLYLeLXLeLee ўQH\(h0L& Ꝥ$`( R \^A&Divide the terms, disregarding thesigns.&If the signs are the same, theanswer is (+). If the signs are different, theanswer is (-). R \ZLl8 ўR HH\`\Z[YS6` tDnitsigneddivision]]ɍuL͟ɍ}RLRɍP\ ڧ[ڧڧbn]ڧvSWI bBBH b1@ kU8  L  Q^R(jQ0l^l\  wUuW ԧ H h@ [_ /QSIRb_L`LLLL`ª`LQLYLeLXLeLee ўQH\(h0L& Ꝥ$`(   ^A&Add the inverse (opposite) of thenumber being subtracted.&If all the signs are the same, usethat sign in the answer. If the signs are mixed, the answerhas the sign of the number whosemagnitude (size) is greater. R \ZLl8 ўR HH\`\Z[YS6` tAnltsignedsubtraction]ɍE}RL(N4<:EP\ ڧ[ڧڧ_k]ڧs}SWI bBBH b1@ kU8  L  Q^R(jQ0l^l\  wUuW ԧ H h@ [_ /QSIRb_L`LLLL`ª`LQLYLeLXLeLee ўQH\(h0L& Ꝥ$`(^A&Multiply all factors together,disregarding the signs.&If the number of negative factorsis even (or if there are none), thesign of the answer is (+). If the number of negative factorsis odd, the sign of the answer is(-). R \ZLl8 ўR HH\`\Z[YS6ʉ t>notsignedmultiplication]BɍRL(N197BP\ ڧ[ڧڧ\h]ڧpzSߠWIߠ b  H b1@ kU8  L  Q^R(jQ0l^l\  wUuW ԧ H h@ [_ /QSIRb_L`LLLL`ª`LQLYLeLXLeLee ўQH\(h0L& Ꝥ$`( magnitude (size) isgreater.^A&If all the signs are the same, addthe numbers and use that sign.If the signs are mixed, add thenumbers with the same signs.&If signs are mixed, subtract thetotals (from Step 1), disregardingthe signs.The answer has the sign of thenumber whose R \ZLl8 ўR HH\`\Z[YS6` tDnitsignedaddition]]ɍuL͟ɍ}RLRɍP\ ڧ[ڧڧbn]ڧvSWI bBBH b1@ kU8  L  Q^R(jQ0l^l\  wUuW ԧ H h@ [_ /QSIRb_L`LLLL`ª`LQLYLeLXLeLee ўQH\(h0L& Ꝥ$`( 3c-2(-2+2c)=33c+4-4c=3-c+4=3-c=-1c=12(1)-d=22-d=2d=0c=1=-433n=-733n=10(10n+2)+1n=100n+20+1n=100n+21-99n=21n=-2199=- 733m=10(- 733)+2m=-7033+2=- 433n=- 7332x-y=3x-2y=-6=4y=5x=2y-62(2y-6)-y=34y-12-y=33y-12=33y=15y=52x-5=32x=8x=4y=52c-d=23c-2d=3=1d=0d=-2+2c+y+y=7416+2y=742y=58y=29x-29=16x=45y=293m-n=52m+n=15=4n=7n=15-2m3m-(15-2m)=53m-15+2m=55m-15=55m=20m=43(4)-n=512-n=5-n=-7n=7m=4b=3a+55a-b=-1a=2b=115a-(3a+5)=-15a-3a-5=-12a-5=-12a=4a=2b=3(2)+5b=6+5b=11a=2m=10n+2n=10m+111z=8-11z=11z=-1y+2(-1)=-1y-2=-1y=1z=-1a-b2=22a-3b=3=94b=12a=2+b22(2+b2)-3b=34+b-3b=34-2b=3-2b=-1b=122a-3(12)=32a-32=32a=92a=94b=12x-y=16x2+y2=37=45y=29x=16+y(16+y) 2+y2=3716m+5n=2m=-3nm=-3n=1(-3n)+5n=22n=2n=1m+5(1)=2m+5=2m=-3n=1r-s=23r+2s=5r=95s=-15r=2+s3(2+s)+2s=56+3s+2s=56+5s=55s=-1s=-15r-(-15)=2r+15=2r=95s=-15y+2z=-13y-5z=8y=1z=-1y=-1-2z3(-1-2z)-5z=8-3-6z-5z=8-3-DDD2  DDD2  D\D2YSTEMS ADD/SUBT@  D\D2YSTEMS SUBSTITڧ[ڧڧz1S_DP\ ڧ[ڧڧzڧڧSH<[H10G/.AͲ] )Y h( ֭  D\D2IND G.C.F.e3zt^  DDD2  DDD2  DDD2  DDD2       =-16n=42m+2(4)=42m+8=42m=-4m=-2n=4-7m-13=2n3n+4m=0m=-3n=4 -7m-2n=13 4m+3n=0-21m-6n=39+ 8m+6n=0-13m=39m=-3-7(-3)-13=2n21-13=2n8=2nn=4m=-32b=-2b=-1a=38x-3y=-22y-x=-1=-5y=-6 8x-3y=-22 -3x+3y=-35x=-25x=-5y-(-5)=-1y+5=-1y=-6x=-55x+6y=166x-5y=7=2y=1 25x+30y=80+ 36x-30y=4261x=122x=25(2)+6y=1610+6y=166y=6y=1x=22m+2n=45m+7n=18m=-2n=4 10m+10n=20- 10m+14n=36-4n=20-20+4n=204n=40n=10m=-2m=4-nn=4+m=0n=4 m+n=4+ -m+n=42n=8n=4m=4-4m=0n=43b-5a=-192a+3b=-5a=2b=-3 -5a+3b=-19- 2a+3b=-5-7a=-14a=22(2)+3b=-54+3b=-53b=-9b=-3a=2a+2b=13a+b=8a=3b=-1 a+2b=1- 6a+2b=16-5a=-15a=33+2b=1a+2b=14a-3b=-11=4b=5 a+2b=14- a-3b=-115b=25b=5a+2(5)=14a+10=14a=4b=5x+2y=53x+2y=17x=6y=-12 x+2y=5- 3x+2y=17-2x=-12x=66+2y=52y=-1y=-12x=610m+4n=2013m-4n=-66m=-2n=10 10m+4n=20+ 13m-4n=-6623m=-46m=-210(-2)+4nD2  DDD2  DDD2  DDD2  D\D2YSTEMS ADD/SUBT@PP\ ڧ[@P\ ڧ[ڧڧzڧڧSH<[H10X]h* ş\[Z QY\[Z8`l6Lş_Ȍb_Ͳ] )Y h( ֭  D\D2IND G.C.F.e3zt^  DDD2  DDD2  DD     1(3y-2)=0(3y-1)(3y-2)=03y-1=03y=1y=133y-2=03y=2y=23y=13(x+1)(x-1)+1=0x=0x2-1+1=0x2=0x=0 21a-3=a-7a=0a=1021=(a-7)(a-3)21=a2-10a+210=a2-10a0=a(a-10)a=0a-10=0a=10a=04=02x=4x=22x+4=02x=-4x=-2x=24m(m+3)+12=3m=-324m2+12m+12=34m2+12m+9=04m2+6m+6m+9=02m(2m+3)+3(2m+3)=0(2m+3)(2m+3)=02m+3=02m=-3m=-329y2=9(y-1)+7y=3y=239y2=9y-9+79y2=9y-29y2-9y+2=09y2-6y-3y+2=03y(3y-2)-b=-524b2+8b-5=04b2+10b-2b-5=02b(2b+5)-1(2b+5)=0(2b-1)(2b+5)=02b-1=02b=1b=122b+5=02b=-5b=-52b=124x2=28xx=x=74x2-28x=04x(x-7)=04x=0x=0x-7=0x=7x=016x2-60=4x=2x=-216x2-64=04(4x2-16)=04(2x-4)(2x+4)=02x-9a2=3aa=0a=139a2-3a=03a(3a-1)=03a=0a=03a-1=03a=1a=13a=02x2+1=9x=2x=-22x2-8=02(x2-4)=02(x-2)(x+2)=0x-2=0x=2x+2=0x=-2x=2a2+6a=-8a=-4a=-a2+6a+8=0(a+4)(a+2)=0a+4=0a=-4a+2=0a=-2a=-44b(b+2)=5b=12D2  DDD2  DDD1  DDD1  D\D1OLVE EQ FACTOR@PP\ ڧ[@P\ ڧ[ڧڧzڧڧSH<[H10Q|#Jx] )Y h( ֭  D\D2IND G.C.F.e3zt^  DDD2  DDD2  DDD2  DDD2  DD    3cd-4d23c(3c+4d)-d(3c+4d)(3c-d)(3c+4d))-1(m+2)(4m-1)(m+2)9cd-4d2+9c2(3c-d)(3c+4d)9cd-4d2+9c2=9c2+9cd-4d29(-4)=-36-36=(-3)(12)-3+12=99c2+9cd-4d2=9c2+12cd-3cd-4d23c(3c+4d)-d(3c+4d)(3c-d)(3c+4d)2=15x2+10xy+6xy+4y25x(3x+2y)+2y(3x+2y)(5x+2y)(3x+2y)4x2-12x+9(2x-3)(2x-3)4*9=3636=6*66+6=124x2-12x+9=4x2-6x-6x+92x(2x-3)-3(2x-3)(2x-3)(2x-3)4m2+7m-2(4m-1)(m+2)4(-2)=-8-8=(-1)(8)-1+8=74m2+7m-2=4m2+8m-m-24m(m+20x2-29x+10=10x2-25x-4x+105x(2x-5)-2(2x-5)(5x-2)(2x-5)x2-5x-50(x+5)(x-10)(1)(-50)=-50-50=(-10)(5)-10+5=-5x2-5x-50=x2-10x+5x-50x(x-10)+5(x-10)(x+5)(x-10)15x2+16xy+4y2(5x+2y)(x+2y)15(4)=6060=6*106+10=1615x2+16xy+4y26(-2)26-2=24a2+24a-52=a2+26a-2a-52a(a+26)-2(a-26)(a-2)(a+26)24k2+7k-6(3k2)(8k-3)(-6)(24)=-144-144=(-9)(16)-9+16=724k2+7k-6=24k2-9k+16k-63k(8k-3)+2(8k-3)(3k+2)(8k-3)10x2-29x+10(5x-)(2x-5)10*10=100100=25*425+4=2918m2-9mn+n2(8m-n)(m-n)8*1=88+1=98m2-9mn+n2=8m2-8mn-mn+n28m(m-n)-n(m-n)(8m-n)(m-n)3b2-5b-2(3b+1)(b-2)3*(-2)=-61*(-6)=-61-6=-53b2-5b-2=3b2-6b+b-23b(b-2)+b-2(3b+1)(b-2)a2+24a-52(a-2)(a+26)(1)(-52)=-52-52=h( ֭  D\D2IND G.C.F.e3zt^  DDD2  D\D2ACTOR TRINOMS_2PP\ ڧ[@P\ ڧ[ڧڧzڧڧSH<[H10lI?@]]]ɍuL͟ɍ}RLRɍg^H8 ^hZLɍR LͲɊRR% QLܤͲ Z@ -^ ş\[Z QY\[Z8`l6Lş_Ȍb_Ͳ] )Y      3y-5x2y(4xy2)=-20x3y3-5x2y(-6y)=30x2y2-15x3y-20x3y3+30x2y25.2c2(.3-1.2c+c2)1.56c-6.24c3+5.2c45.2c2(.3)=1.56c25.2c2(-1.2c)=-6.24c35.2c2(c2)=5.2c41.56c2+6.24c3+5.2c4x(14)= 112x13x3-16x2+ 112x-6.1y(3-.2y-.1y2)-18.3y+1.22y2+.61y3-6.1y(3)=-18.3y-6.1y(-.2y)=1.22y2-6.1y(-.1y2)=.61y3-18.3y+1.22y2+.61y3-5x2y(3x+4xy2-6y)-15x3y-20x3y3+30x2y2-5x2y(3x)=-15x17+ 114-1)mn=( 214+ 114-1414)mn-1114mn-3x2y2-(-5xy2)-x2y2-4x2y2+5xy2-3x2y2+(-x2y2)+5xy2(-3-1)x2y2+5xy2-4x2y2+5xy22b-4ab2a2b-2a2b-4ab2=a2b+(-2a2b)-4ab2(1-2)a2b-4ab2-a2b-4ab2-4a2-(-.6a)-7.1a-4a2-6.5a-4a2-(-.6a)-7.1a=-4a2+.6a-7.1a-4a2+(-7.1+.6)a-6.5a-4a217mn-(- 114mn)-mn-1114mn17mn+ 114mn+(-mn)(14a2b2+a2b11a2b2-(-3a2b2)=11a2b2+3a2b2(11+3)a2b2=14a2b2-(-a2b)=a2b14a2b2+a2b51x-16y-16x-(-5y)35x-11y51x-16x=51x+(-16x)(51-16)x=35x-16y-(-5y)=-16y+5y(-16+5)y=-11y35x-11ya2b-4ab2-2a2b-a^A&Arrange each polynomial in the sameorder.&Multiply each term of onepolynomial by each term of theother.Use the FOIL (First, Outer,Inner, Last) method.&Write the products as a singleexpression.&Add like terms.R \ZLl8 ўR HH\`\Z[YS6` t@nmtpolymultiplicationE+(N(N4<:EP\ ڧ[ڧڧ^j]ڧr|SWI b$ H b10 kU8  L  Q^R(jQ0l^l\  wUuW ԧ H h@ [_ /QSIRb_L`LLLL`ª`LQLYLeLXLeLee ўQH\(h0L& Ꝥ$`(    itsinverse to both sides.&Divide both sides of the equationby the coefficient of the variable.If the coefficient is a fraction,multiply both sides of the equationby the reciprocal of that fraction.^A&Simplify each side of the equationby combining like terms.&Rewrite the equation so that thevariable is on one side of theequation, and all other terms areon the other side of the equation.RULE: To remove a term from oneside of an equation, add R \ZLl8 ўR HH\`\Z[YS6` tAtltfirstwithconstant]ɍuLHRR(N7?=P\ ڧ[ڧڧ_k]ڧs}SWI b$ H b1@ kU8  L  Q^R(jQ0l^l\  wUuW ԧ H h@ [_ /QSIRb_L`LLLL`ª`LQLYLeLXLeLee ўQH\(h0L& Ꝥ$`(+21a8a2+6a2=(8+6)a2=14a214a+7a=(14+7)a=21a14a2+21a0bc(14+15)bc=( 520+ 420)bc 920bc6x3y2+4x2y3+3x3y2+7x2y39x3y2+11x2y36x3y2+3x3y2=(6+3)x3y2=9x3y24x2y3+7x2y3=(4+7)x2y3=11x2y39x3y2+11x2y38a2+14a+6a2+7a14a2xy24x2y+7x2y=(4+7)x2y=11x2y6xy2+11xy2=(6+11)xy2=17xy211x2y+17xy22.6ab+4.5ab7.1ab(2.6+4.5)ab7.1ab20c2+35c+15c2+5c35c2+40c20c2+15c2=(20+15)c2=35c235c+5c=(35+5)c=40c35c2+40c14bc+15bc9211b+2b+7b20b(11+2+7)b20b3x+y+2x+5y5x+6y3x+2x=(3+2)x=5xy+5y=(1+5)y=6y5x+6y.63c+.1c+2.2c2.93c(.63+.1+2.2)c2.93c11b3+b2+9b320b3+b211b3+9b3=(11+9)b3=20b320b3+b24x2y+6xy2+7x2y+11xy211x2y+17\D2DD SIGNEDTe3zt^  DDD2  DDD2  D\D2DD MONOMIALS[@PP\ ڧ[@P\ ڧ[ڧڧzڧڧSH<[H10$_^6DRɍg^H8 ^hZLɍR LͲɊRR% QLܤͲ Z@ -^ ş\[Z QY\[Z8`l6Lş_Ȍb_Ͳ] )Y h( ֭  D2m2n32n2(mn2)=2mn42mn3-2m2n3+2mn43xy(x2-2y2)3x3y-6xy33xy(x2)=3x3y3xy(-2y2)=-6xy33x3y-6xy313x(x2-12x+14)13x3-16x2+112x13x(x2)=13x313x(-12x)=-16x213-4rs)=-16r3s24r2s(3)=12r2s12r4s3-16r3s2+12r2s-9z(-3+8z-9z2)27z-72z2+81z3-9z(-3)=27z-9z(8z)=-72z2-9z(-9z2)=81z327z-72z2+81z32n2(mn-m2n+mn2)2mn3-2m2n3+2mn42n2(mn)=2mn32n2(-m2n)=-a2(2a+5)2a+5a2a2(2a)=2a3a2(5)+5a22a3+5a2-x2(3x2-2x4)-3x4+2x6-x2(3x2)=-3x4-x2(-2x4)=2x6-3x4+2x64r2s(3r2s2-4rs+3)12r4s3-16r3s2+12rs4r2s(3r2s2)=12r4s34r2s(Z8`l6Lş_Ȍb_Ͳ] )Y h( ֭  DDD2  D\D2ULT. POLYXMONOt^editPP\ ڧ[@P\ ڧ[ڧڧzڧڧSH<[H10 IE92[YS6`LxQɿu3'RͲʎRʎ]]]ɍuL͟ɍ}RLRɍg^H8 ^hZLɍR LͲɊRR% QLܤͲ Z@ -^ ş\[Z QY\[        8c+3=-8c+3-3=-8-3c=-111=34(8-x)+1x=81=6-34x+11=7-34x-7+1=7-7-34x-6=-34x-6(-43) = -34x(-43)x=8-5c+2(c+4)-6=-19c=7-5c+2c+8-6=-19-3c+2=-19-3c+2-2=-19-2-3c=-21-3c- 3 = -21- 3c=7-6+6=0+612a=6(12a)2=6*2a=12a4 = 34a=3(a4)4 = 34(4)a=33(y-1)+2y=8y=1153y-3+2y=85y-3=85y-3+3=8+35y=115y 5=11 5y=11 52(a+3)-6=0a=02a+6-6=02a = 02a 2 = 02a=03c-(2c-3)=-8c=-113c-2c+3=-    5a-12=33a=95a-12+12=33+125a=455a 5=45 5a=9y4-2=6y=32y4-2+2=6+2y4=8(y4)4=8*4y=325(m-2)-2m+21=-1m=-45m-10-2m+21=-13m+11=-13m+11-11=-1-113m=-123m 3 = -12 3m=-4a-12a-6=0a=1212a-6=012aD2  DDD2  DDD2  DDD2  D\D2OLVE 1ST W/CON@PP\ ڧ[@P\ ڧ[ڧڧzڧڧSH<[H10>y'U Z@ -^ ş\[Z QY\[Z8`l6Lş_Ȍb_Ͳ] )Y h( ֭  D\D2IND G.C.F.e3zt^  DDD2  DD  -12=42y=54y-12+12=42+12y=5425=a+6a=1925-6=a+6-6a=199=c+36c=-279-36=c+36-36c=-27a-5=11a=16a-5+5=11+5a=1621=x-14x=3521+14=x-14+14x=35m+31=17m=-14m+31-31=17-31m=-144+n=27n=23-4+4+n=27-4n=2330=y+45y=-1530-45=y+45-45y=-15m-17=21m=38m-17+17=21+17m=38a+11=-3a=-14a+11-11=-3-11a=-14yD2  DDD2  DDD2  DDD2  D\D2OLVE 1RST ڧ[@PP\ ڧ[@P\ ڧ[ڧڧzڧڧSH<[H=c2d2GCF = 4c2d24y318y22y24=2*218=2*3*3G.C.F. = 2y3=y*y*yy2=y*yG.C.F. = y*y = y2G.C.F. = 2y2=x*xx=xG.C.F. = xG.C.F. = 125x6x2y11x2y2x2y6=6*111=11*1G.C.F. = 1x2y=x*x*yx2y2=x*x*y*yG.C.F. = x2y12c2d364c3d24c2d212=2*2*364=2*2*2*2*2*2GCF = 2*2 = 4c2d3=c*c*d*d*dc3d2=c*c*c*d*dGCF = c*c*d*d 12d12=2*2*336=2*2*3*3G.C.F. = 2*2*3 = 12d2=d*dcd=cdG.C.F. = dG.C.F. = 12d35m2n70n235n35=5*770=2*5*7G.C.F. = 5*7 = 35m2n=m*m*nn2=n*nG.C.F. = nG.C.F. = 35n125x2625x125x125=5*5*5625=5*5*5*5G.C.F. = 5*5*5 = 125x2*2*3*5G.C.F. = 2*2*3 = 12r2s2=r*r*s*sr3s=r*r*r*sG.C.F. =r*r*s = r2sG.C.F. = 12r2s80a4b352a2b4a2b80=2*2*2*2*552=2*2*13G.C.F. = 2*2 = 4a4b3=a*a*a*a*b*b*ba2b=a*a*bG.C.F. = a*a*b = a2bG.C.F. = 4a2b12d236cd18y3 24y26y218=2*3*324=2*2*2*3G.C.F. = 6y3=y*y*yy2=y*yG.C.F. = y*y = y2G.C.F. = 6y27m2n56mn27mn7=1*756=2*2*2*7G.C.F. = 7m2n=m*m*nmn2=m*n*nG.C.F. = mnG.C.F. = 7mn12r2s260r3s12r2s12=2*2*360=2 ş\[Z QY\[Z8`l6Lş_Ȍb_Ͳ] )Y h( ֭  D\D2IND G.C.F.e3zt^editE eKt^editP\ ڧ[ڧڧzڧڧSH<[H10sdW$R HH\`\Z[YS6`LxQɿu3'RͲʎRʎ]]]ɍuL͟ɍ}RLRɍg^H8 ^hZLɍR LͲɊRR% QLܤͲ Z@ -^     10$Hn#CgRR% QLܤͲ Z@ -^ ş\[Z QY\[Z8`l6Lş_Ȍb_Ͳ] )Y h( ֭  D\D2IND G.C.F.e3zt^  DD    -4x2(6xy2x)(6xy-2x)@(36x2y2) = 6xy @(4x2) = 2x(6xy+2x)(6xy-2x)@(49m2) = 7m@(64n2) = 8n(7m+8n)(7m-8n)625y6-225(25y315)(25y3-15)@(625y6) = 25y3@(225) = 15(25y3+15)(25y3-15)y2-49(y23)(y-23)@(y2) = y@(49) = 23(y+23)(y-23)-4x2+36x2y2=36x2y2)@(a2) = a@( 925) = 35(a+35)(a-35)4y6-9(2y33)(2y3-3)@(4y6) = 2y3@(9) = 3(2y3+3)(2y3-3)-36a2+49b2=49b2-36a2(7b6a)(7b-6a)@(49b2) = 7b@(36a2) = 6a(7b+6a)(7b-6a)49m2-64n2(7m8n)(7m-8n)16x2-1(4x1)(4x-1)@(16x2)=4x@1=1(4x+1)(4x-1)a2-36b2(a6b)(a-6b)@(a2)=a@(36b2)=6b(a+6b)(a-6b)81x2-121y4(9x11y2)(9x-11y2)@(81x2) = 9x@(121y4) = 11y2(9x+11y2)(9x-11y2)a2- 925(a35)(a-35\D2IND G.C.F.e3zt^  DDD2  DDD2  D\D2IFF. 2 SQUARES@PP\ ڧ[@P\ ڧ[ڧڧzڧڧSH<[H10<|82QRɍg^H8 ^hZLɍR LͲɊRR% QLܤͲ Z@ -^ ş\[Z QY\[Z8`l6Lş_Ȍb_Ͳ] )Y h( ֭  Dx+453(5x2-6x+15)G.C.F. = 3(15x2-18x+45)%3=5x2-6x+153(5x2-6x+15)8a2b3-2a2b2+6ab22ab2(4ab-a+3)G.C.F.=2ab2(8a2b3-2a2b2+6ab2)%2ab2=(4ab-a+3)2ab2(4ab-a+3)%13y=-1+2y+3y213y(-1+2y+3y2)4cd+8c2d2+12c3d34cd(1+2cd+3c2d2)G.C.F.=4cd(4cd+8c2d2+12c3d3)%4cd=(1+2cd+3c2d2)4cd(1+2cd+3c2d2)25ab-5a2b25ab(5-ab)G.C.F. = 5ab(25ab-5a2b2)%5ab=5-ab5ab(5-ab)15x2-18v2+3uv)2yz2-6y2z2yz(z-3y)G.C.F. = 2yz(2yz2-6y2z)%2yz=z-3y2yz(z-3y)12a2b+16ab2-4ab4ab(3a+4b-1)G.C.F.=4ab(12a2b+16ab2-4ab)%4ab=3a+4b-14ab(3a+4b-1)-13y+26y2+39y313y(-1+2y+3y2)G.C.F. = 13y(-13y+26y2+39y3)4a2-aa(4a-1)G.C.F. = a(4a2-a)%a = 4a-1 a(4a-1)9r2-27r2s9r2(1-3s)G.C.F. = 9r2(9r2-27r2s)%9r2=1-3s9r2(1-3s)-50u2+25v2+75uv25(-2u2+v2+3uv)G.C.F. = 25(-50u2+25v2+75uv)%25=-2u2+v2+3uv25(-2u2+_Ͳ] )Y h( ֭  D\D2IND G.C.F.e3zt^  D\D2ACTOR POLYS ڧ[ڧڧz1S_2P\ ڧ[ڧڧzڧڧSH<[H10[@ X$QxQɿu3'RͲʎRʎ]]]ɍuL͟ɍ}RLRɍg^H8 ^hZLɍR LͲɊRR% QLܤͲ Z@ -^ ş\[Z QY\[Z8`l6Lş_Ȍb     (-13m2)-(-12n2)56m2-12n212m2-(-13m2)=12m2+13m2(12+13)m2=(36+26)m2=56m2-n2-(-12n2)=-n2+12n2(-1+12)n2=-12n256m2-12n211a2b2-(-3a2b2)-(-a2b)5a-12a-7a5a+(-12a)(5-12)a-7a16c-8d-4c-(-d)12c-7d16c-4c=16c+(-4c)(16-4)c=12c-8d-(-d)=-8d+d(-8+1)d=-7d12c-7d4.6a-(-1.7a)-2b-(-b)6.3a-b4.6a-(-1.7a)=4.6a+1.7a(4.6+1.7)a=6.3a-2b-(-b)=-2b+b(-2+1)b=-b6.3a-b12m2-n2-_Ͳ] )Y h( ֭  D\D2DD POLYNOMIALS3zt^  D\D2UBT MONOMIALSڧ[ڧڧz9S_9P\ ڧ[ڧڧzڧڧSH<[H10[*[<xQɿu3'RͲʎRʎ]]]ɍuL͟ɍ}RLRɍg^H8 ^hZLɍR LͲɊRR% QLܤͲ Z@ -^ ş\[Z QY\[Z8`l6Lş_Ȍb    !5b2)+(6a2-7ab+b2)15a2-7ab-4b2(9a2-5b2)+(6a2-7ab+b2)(9a2+6a2)=(9+6)a2=15a2-5b2+b2=(-5+1)b2=-4b215a2-7ab-4b212x3+23x+1)+(-12x2+14x+6)23x+14x=(23+14)x=( 812+ 312)x=1112x1+6=712x3-12x2+1112x+7(.8z2+4.1z)+(.9z-5z2)-4.2z2+5z.8z2-5z2=(.8-5)z2=-4.2z24.1z+.9z=(4.1+.9)z=5z-4.2z2+5z(9a2-(.3x+y)+(5x+2y-z)5.3x+3y-z.3x+5x=(.3+5)x=5.3xy+2y=(1+2)y=3y5.3x+3y-z(4m2-3mn)+(-3m2+mn)m2-2mn4m2+(-3m2)=(4-3)m2=m2-3mn+mn=(-3+1)mn=-2mnm2-2mn(12x3+23x+1)+(6-12x2+14x)12x3-12x2+1112x+7(d=5cd7c+5cd+d(6.3m-.8)+(2.1m+6.3)8.4m+5.56.3m+2.1m=(6.3+2.1)m=8.4m-.8+6.3=6.3-.8=5.58.4m+5.5(12x+23y)+(13x-13y)56x+13y12x+13x=(12+13)x=(36+26)x=56x23y-13y=(23-13)y=13y56x+13y(2a+4)+(a+7)3a+112a+a=(2+1)a=3a4+7=113a+11(3a2-2ab)+(a2+ab+b)4a2-ab+b3a2+a2=(3+1)a2=4a2-2ab+ab=(-2+1)ab=-ab4a2-ab+b(8c+6cd-d)+(2d-c-cd)7c+5cd+d(8c+6cd-d)+(-c-cd+2d)8c-c=(8-1)c=7c-d+2d=(-1+2)d=d6cd-cd=(6-1)c ş\[Z QY\[Z8`l6Lş_Ȍb_Ͳ] )Y h( ֭  D\D2DD POLYNOMIALS3zt^editE eKt^editP\ ڧ[ڧڧzڧڧSH<[H108jPўR HH\`\Z[YS6`LxQɿu3'RͲʎRʎ]]]ɍuL͟ɍ}RLRɍg^H8 ^hZLɍR LͲɊRR% QLܤͲ Z@ -^     n)(23n2)(13n3)19n6(12*23*13)(n*n2*n3)19n6(a2)2(3a)3a5(a4)(3a)=3(a4*a)3a5(3x)2(x2)39x8(9x2)(x6)=9(x2*x6)9x8(16x3)(12x)(-2x3)-4x7[16*12*(-2)](x3*x*3)-4x7(0.2m2)(4m2)(5m)4m5(0.2*4*5)(m2*m2*m)4m5(4ab)(a2b)4a3b2(4)(a*a2)(b*b)4a3b2(11m)(-2n)(3mn)-66m2n2[11*(-2)*3](m*m)(n*n)-66m2n2(12(3y2)(-4y)-12y3(3y2)(-4y)=[3*(-4)](y2*y)-12y3(5b2)(-5b)2125b4(5b2)(25b2)=(5*25)(b2*b2)125b4(3ab)2(2a3b)3(-2a)-144a12b5(9a2b2)(8a9b3)(-2a)[9*8*(-2)](a2*a9*a)(b2*b3)-144a12b5 ş\[Z QY\[Z8`l6Lş_Ȍb_Ͳ] )Y h( ֭  D\D2ULT. MONOMIALS3zt^editE eKt^editP\ ڧ[ڧڧzڧڧSH<[H10CGSўR HH\`\Z[YS6`LxQɿu3'RͲʎRʎ]]]ɍuL͟ɍ}RLRɍg^H8 ^hZLɍR LͲɊRR% QLܤͲ Z@ -^ab-1.7b(6z2-10)-(7z2+6z-2)-z2-6z-86z2-(7z2)=6z2+(-7z2)(6-7)z2=-z2-10-(-2)=-10+2=-8-(+6z)=-6z-z2-6z-8x2+y2-(x2-y2)2y2x2-(x2)=x2+(-x2)(1-1)x2=0y2-(-y2)=y2+y22y2-2z5x+2y-2z(4n2+n-1)-(2n2+1)2n2+n-24n2-(2n2)=4n2+(-2n2)(4-2)n2=2n2-1-(+1)=-1+(-1)=-22n2+n-2(.6a-b)-(2a-3ab+.7b)-1.4+3ab-1.7b.6a-(2a)=.6a+(-2a)(.6-2)a=-1.4a-b-(.7b)=-b+(-.7b)(-1-.7)b=-1.7b-(-3ab)=3ab-1.4a+3y(.9a-2.1b)-(.8a+.8b).1a-2.9b.9a-(.8a)=(.9-.8)a(.9-.8)a=.1a-2.1b-.8b=-2.1b+(-.8b)(-2.1-.8)b=-2.9b.1a-2.9b(6x-3y+2z)-(4z-5y+x)5+2y-2z(6x-3y+2z)-(x-5y+4z)6x-x=6x+(-x)(6-1)x=5x-3y-(-5y)=-3y+5y(-3+5)y=2y2z-(4z)=2z+(-4z)(2-4)z=2)=3y2+y2(3+1)y2=4y2x2-5xy+4y2(15x+13y)-(23y+25x)-15-13y(15x+13y)-(25x+23y)15x-25x=15x+(-25x)(15-25)x=-15x13y-23y=13y+(-23y)(13-23)y=-13y-15x-13(3a+b)-(4a+2b)--b3a-(4a)=3a+(-4a)(3-4)a=-ab-(2b)=b+(-2b)(1-2)b=-b-a-b(5m-15)-(2m-6)3m-95m-(2m)=5m+(-2m)(5-2)m=3m-15-(-6)=-15+6=-93m-9(x2-xy+3y2)-(-y2+4xy)x2-5xy+4y2-xy-(4xy)=-6xy+(-4xy)(-1-4)xy=-5xy3y2-(-y[Z8`l6Lş_Ȍb_Ͳ] )Y h( ֭  D\D2E  D\D2UBT POLYNOMIALSt^editP\ ڧ[ @P\ ڧ[ڧڧzڧڧSH<[H10X2z [YS6`LxQɿu3'RͲʎRʎ]]]ɍuL͟ɍ}RLRɍg^H8 ^hZLɍR LͲɊRR% QLܤͲ Z@ -^ ş\[Z QY\z"#Ԡ Š Ҡ Π  Π ӠԠƠ Π ߲Ӡ٠Ӡ٠Π Π ΠΠΠ Π Π Š Ԡ Ҡ   Π  ΠΠ!Ԡ Π Ơ ٠ ߲Ӡ Ӡ!٠  Π Π Π Π Π  Π Π  ŠԠҠ  ΠΠΠ  ΠԠΠƠ ٠߲Ӡ٠  ΠΠΠ ΠΠΠΠ  Ӡ٠ҠŠԠ  Π Π ΠԠ ΠƠ ٠ ߲Ӡ ΠΠΠ ΠΠΠΠ.cret.swit.shlx.asrx.psh.lpsh.pop.lpop.mulx.divx.modx.cpystk2.calip4hp4pxn4 sYbbsh65.libnthnm.26 cRh{Rdx $?[_isspace__Top_settop_.fstswt.mul.div.udv.mod.umd.move.shl.asr.shr.cpystk.modstk.csav -613-(-23)-523-16.6-(+7.4)-2463.8-(-31.7)95.5-27.7-(-36.6)8.9-106.5-(-29.9)-76.6ompa10-(+7)315-(-9)24-23-(+17)-40-16-(+8)-24-7-(-5)-2-42-(-21)-2198-(-29)12719-(-62)81607-(+49)558-136-(-47)-8987-5829-531-(-107)-424434-(114)3121313-(423)823912-(-214)1134ret.swit.shlx.asrx.psh.lpsh.pop.lpop.mulx.divx.modx.cpystk2.calip4hp4pxn4 sYbbsh65.libnthnm.26 cRdx $?[_isspace__Top_settop_.fstswt.mul.div.udv.mod.umd.move.shl.asr.shr.cpystk.modstk.csav.c.23+(-11.3)-27.53-101.1+80.6-20.5-5.1+(-31.6)+(-16.8)-53.5-107+(-29)+47-892115+(-1625)+192345-712+(-313)+412-613720+(-360)+(-473)+15-98.006+(-1.1)+(-.07)-1.164act55+78133-6+(-7)-13-15+(-23)-3822+7+1544-8+(-9)+(-5)-22125+51+201377-215+(-2015)+(-15)-2245-206+400194-614+(-534)-124+1115+7252235-712+513-216-716+(-1156)+(-313)-2213-16.swit.shlx.asrx.psh.lpsh.pop.lpop.mulx.divx.modx.cpystk2.calip4hp4pxn4 sYbbsh65.libnthnm.26 c[z7h+db{(C]w&H]_isspace__Top_settop_.fstswt.mul.div.udv.mod.umd.move.shl.asr.shr.cpystk.modstk.csav7n3-x)+(2x2-6x3+7)x4-3x3+2x2-x+7(4.3x-.7)+(7.8x+6.4)12.1x+5.7(.6z2+3.7z)+(.4z-9z2)-8.4z2+4.1z(13x-14y)+(14x+34y)712x+12y(.7z2+6.2z)+(.8z-12z2)-11.3z2+7z(25m-37n)+(13m+57n)1115m+2ab2)ab(4a+7ab-b)+(-a-ab+2b)3a+6ab+b(6mn+5m2)+(11m2-4mn)16m2+2mn(x2y-xy)+(xy2+xy+y2)x2y+xy2+y2(.6a+.2b-c)+(.4c-8a)-7.4a+.2b-.6c(.6x+y)+(7x+4y-3z)7.6x+5y-3z(3m2-7n2)+(m2-9mn+9n2)4m2-9mn+2n2(x4+3x x-(3b+7)+(b+8)4b+15(5x+1)+(6+x)6x+7(6x2-2x+1)+(x2-1)7x2-2x(y2-1)+(16-8y+y2)2y2-8y+15(a2+2a-6)+(7-a2)2a+1(4ab-15)+(a2b2+6ab-1)a2b2+10ab-16(5x2-7xy)+(x2+4xy+y2)6x2-3xy+y2(a2b+ab2)+(ab-a2b-cret.swit.shlx.asrx.psh.lpsh.pop.lpop.mulx.divx.modx.cpystk2.calip4՞۞םn4sn4om4 sYbbsh65.libelnm.26 ci.m*settop_.fstswt.mul.div.udv.mod.umd.move.shl.asr.shr.cpystk.modstk.csav.cret.swit.shlx.asrx.psh   (xyz)(-x2z)(yz2)(2z)2-4x3y2z6(.1n)2(-4n)(m2)-.04m2n3(mn)m5n7(4b)(-2b2)3-32b7(4xy)(-2x2)(-3xy2)2-72x5y5(13m)(23n)(mn2)29m2n3(4x2y)2(3x)3432x7y2(4.1x)(-.6x)(x2)-2.46x4(-.7y)(-4.3y)(y2)3.01y4(-19x)(x2y)2(3y)3-3x5y5tx2*x3x5a3*a*a4a8y*y4y5b2*b*b3b6(2x)(-xy)-2x2y(x2y)(xy2)x3y3(7x2y)(-xy2)-7x3y3(z2)(-z)(-z3)(-z4)-z10(-k2)(k)(k2)4-k11(mn2)(2mn)(m3n)2m5n4(m2n3)2.cret.swit.shlx.asrx.psh.lpsh.pop.lpop.mulx.divx.modx.cpystk2.calip4՞۞םn4sn4om4 sYbbsh65.libelnm.26 c<20 (6I]w+S{/R(C]w&H]_isspace__Top_settop_.fstswt.mul.div.udv.mod.umd.move.shl.asr.shr.cpystk.modstk.csav )712m-32n2a-5)2a2-3a-4(.7x-y)-(3x-6xy+.4y)-2.3x+6xy-1.4y(3.3a2-.6a)-(1.4a-a2)4.3a2-2a(.4a-3.7b)-(.3a+.7b).1a-4.4b(13c+15d)-(25d+12c)-16-15d(13m-n2)-(12n2-14m)712m-32n22b-b2-2b2(9xy-x2y2)-(x2y2+xy-y)-2x2y2+8xy+y(x2y-xy)-(-x2-x2y+2xy)x2+2x2y-3xy(4m2+2mn)-(7m2n-3m2)7m2-7m2n+2mn(mn-1)-(m2n2+mn-n2-1)-m2n2+n2(3x-4y+7z)-(5z-8y+x)2+4y+2z(6a2-9)-(4a2+31 (x+y)-(x-y)2y(5a+2b)-(3a+b)2a+b(x-5)-(x+7)-12(y2+z2)-(y2-z2)2z2(7c-17)-(5c-11)2c-6(a2+b)-(b-a2)2a2(4x2+x-3)-(3x2+1)x2x-4(m2-mn+5n2)-(-n2+7mn)m2-8mn+6n2(4a2b-b2)-(b2+ab2-a2b)5at.swit.shlx.asrx.psh.lpsh.pop.lpop.mulx.divx.modx.cpystk2.calip4hp4pxn4 sYbbsh65.libnthnm.26 ckRR% QLܤͲ Z@ -^ ş\[Z QY\[Z8`l6Lş_Ȍb_Ͳ] )Y h( ֭  D\D2E  D\D2C_SQUARESeKt^e  25*5*10125025*5=125125*10125045*23*7871545*23*78=15*13*71715(.01)(2.7).027(.01)*(2.7).027(-8)(-7)568*756(-17)(-29)26317*29263(7)(-3)-217*3=21-21(23)(D2  DDD2  DDD2  DDD1  D\D1ULT. SIGNEDڧ[@PP\ ڧ[@P\ ڧ[ڧڧzڧڧSH<[H10)s?p8`l6Lş_Ȍb_Ͳ] )Y h( ֭  D\D2IND G.C.F.e3zt^  DDD2  DDD2  DDD2  DD     15x2-6015x2-60=15(x2-4)=15(x+2)(x-2)20x2+8x-1220x2+8x-12=4(5x2+2x-3)=4(5x+3)(x-1)\D2E  D\D2C_SQUARESeKt^e  DDD2  D\D2C_POLY_COMPLETES_2PP\ ڧ[@P\ ڧ[ڧڧzڧڧSH<[H2]4m]ɍuL͟ɍ}RLRɍg^H8 ^hZLɍR LͲɊRR% QLܤͲ Z@ -^ ş\[Z QY\[Z8`l6Lş_Ȍb_Ͳ] )Y h( ֭  D-.004)940-3.76-.004-3.76-.004=-3760 - 4940(- 711)%(-4944)47(- 711)*(-4449)(- 711)*(-4449)=(-11)*(-47)47(-18)%3-6-18 3-6(-10.8)%(.02)-540-10.8 .02=-1080 2-540( 922)%(-125%5525 5=51523%477623*74=13*7276412%.41030412.4412.4=4120 41030(-33)%(-11)3-33-113-45%-89910-45*(-98)-45*(-98)=-15*(-92)910(-3.76)%(h( ֭  D\D2DD SIGNEDTe3zt^  DDD2  D\D2IVIDE SIGNEDS_9PP\ ڧ[@P\ ڧ[ڧڧzڧڧSH<[H10S=U]]]ɍuL͟ɍ}RLRɍg^H8 ^hZLɍR LͲɊRR% QLܤͲ Z@ -^ ş\[Z QY\[Z8`l6Lş_Ȍb_Ͳ] )Y    !!-6)-13823*6=138-138(-11)(-2)(-3)-6611*2*3=66-66(100.1)(-.3)-30.03(100.1)(.3)=30.03-30.03(250)(-5)(-10)(-4)-50000250*5*10*4=50000-500002x-10=y5x-3y=22y=2x-105x-3(2x-10)=225x-6x+30=22x=82(8)-10=y so y=6 r-s=23r+2s=5r-s=2 so r=2+s 3(2+s)+2s=56+3s+2s=55s=-1 so s=-15r-(-15)=2 so r=95( ֭  D\D2E  DDD2  DDD2  D\D2NEAR_SUBSTITUTE@PP\ ڧ[@P\ ڧ[ڧڧzڧڧSH<[H2uSͲʎRʎ]]]ɍuL͟ɍ}RLRɍg^H8 ^hZLɍR LͲɊRR% QLܤͲ Z@ -^ ş\[Z QY\[Z8`l6Lş_Ȍb_Ͳ] )Y h 5x=4y3x-4y=8 5x-4y=0- 3x-4y=8 2x=-8x=-45(-4)=4y so y=-58x-3y=-32y-x=-1 8x-3y=-32+ -3x+3y= -3 5x=-35x=-7y-(-7)=-1 so y=-8Ͳ] )Y h( ֭  D\D2E  DDD2  D\D2NEAR_ADD_SUB PP\ ڧ[@P\ ڧ[ڧڧzڧڧSH<[H2L6`LxQɿu3'RͲʎRʎ]]]ɍuL͟ɍ}RLRɍg^H8 ^hZLɍR LͲɊRR% QLܤͲ Z@ -^ ş\[Z QY\[Z8`l6Lş_Ȍb_Z8`l6Lş_Ȍb_Ͳ] )Y h( ֭  DDD2  D\D2ULT. POLYXMONOt^editPP\ ڧ[@P\ ڧ[ڧڧzڧڧSH<[H10 IE92[YS6`LxQɿu3'RͲʎRʎ]]]ɍuL͟ɍ}RLRɍg^H8 ^hZLɍR LͲɊRR% QLܤͲ Z@ -^ ş\[Z QY\[!!""" " " " "" """""""" ab-1.7b(6z2-10)-(7z2+6z-2)-z2-6z-86z2-(7z2)=6z2+(-7z2)(6-7)z2=-z2-10-(-2)=-10+2=-8-(+6z)=-6z-z2-6z-8x2+y2-(x2-y2)2y2x2-(x2)=x2+(-x2)(1-1)x2=0y2-(-y2)=y2+y22y2-2z5x+2y-2z(4n2+n-1)-(2n2+1)2n2n-24n2-(2n2)=4n2+(-2n2)(4-2)n2=2n2-1-(+1)=-1+(-1)=-22n2+n-2(.6a-b)-(2a-3ab+.7b)-1.4+3ab-1.7b.6a-(2a)=.6a+(-2a)(.6-2)a=-1.4a-b-(.7b)=-b+(-.7b)(-1-.7)b=-1.7b-(-3ab)=3ab-1.4a+3y(.9a-2.1b)-(.8a+.8b).1a-2.9b.9a-(.8a)=(.9-.8)a(.9-.8)a=.1a-2.1b-.8b=-2.1b+(-.8b)(-2.1-.8)b=-2.9b.1a-2.9b(6x-3y+2z)-(4z-5y+x)5+2y-2z(6x-3y+2z)-(x-5y+4z)6x-x=6x+(-x)(6-1)x=5x-3y-(-5y)=-3y+5y(-3+5)y=2y2z-(4z)=2z+(-4z)(2-4)z=2)=3y2+y2(3+1)y2=4y2x2-5xy+4y2(15x+13y)-(23y+25x)-15-13y(15x+13y)-(25x+23y)15x-25x=15x+(-25x)(15-25)x=-15x13y-23y=13y+(-23y)(13-23)y=-13y-15x-13(3a+b)-(4a+2b)--b3a-(4a)=3a+(-4a)(3-4)a=-ab-(2b)=b+(-2b)(1-2)b=-b-a-b(5m-15)-(2m-6)3m-95m-(2m)=5m+(-2m)(5-2)m=3m-15-(-6)=-15+6=-93m-9(x2-xy+3y2)-(-y2+4xy)x2-5xy+4y2-xy-(4xy)=-6xy+(-4xy)(-1-4)xy=-5xy3y2-(-y[Z8`l6Lş_Ȍb_Ͳ] )Y h( ֭  D\D2E  D\D2UBT POLYNOMIALSt^editP\ ڧ[ @P\ ڧ[ڧڧzڧڧSH<[H10X2z [YS6`LxQɿu3'RͲʎRʎ]]]ɍuL͟ɍ}RLRɍg^H8 ^hZLɍR LͲɊRR% QLܤͲ Z@ -^ ş\[Z QY\511)-310 922*(-1115) 922*(-1115)=32*(-15)- 310+2)8a4+14a2-4=2(4a4+7a2-2)4(-2)=-88(-1)=-88-1=74a4+7a2-2=4a4+8a2-a2-24a2(a2+2)-(a2+2)(4a2-1)(a2+2)(2a+1)(2a-1)(a2+2)2(2a+1)(2a-1)(a2+2)-9b)+5b(a-9b)=(a+5b)(a-9b)b(a+5b)(a-9b)7xy-y2+18x2(9xy)(2x+y)7xy-y2+18x2=-y2+7xy+18x218x2+7xy-y218(-1)=-18-2*9=-18-2+9=718x2+7xy-y2=18x2+9xy-2xy-y29x(2x+y)-y(2x+y)(9x-y)(2x+y)8a4+14a2-42(2a1)(2a-1)(a2m-1)(m+1)(m2-3)m(m-1)(m+1)(m2-3)6x2-24y26(x2y)(x+2y)6x2-24y2=6(x2-4y2)6(x-2y)(x+2y)a2b-4ab2-45b3b(a+5b)(a9b)a2b-4ab2-45b3=b(a2-4ab-45b2)-45*1=-45-9+5=-4-9*5=-45a2-4ab-45b2=a2-9ab+5ab-45b2a(a2-2yz+z2)1*1=11+1=2y2-2yz+z2=y2-yz-yz+z2y(y-z)-z(y-z)=(y-z)(y-z)=(y-z)29y(y-z)2m5-4m3+3mm(m1)(m+1)(m2-3)m5-4m3+3m=m(m4-4m2+3)3*1=33+1=4m4-4m2+3=m4-3m2-m2+3m2(m2-3)-(m2-3)=(m2-1)(m2-3)(x3-xy2x(xy)(x-y)x3-xy2=x(x2-y2)x(x+y)(x-y)3a2-3a-603(a4)(a-5)3a2-3a-60=3(a2-a-20)-20*1=-20-5*4=-20-5+4=-1a2-a-20=a2-5a+4a-203a(a-5)+12(a-5)3(a+4)(a-5)9y3-18y2z+9yz29y(y-z)29y3-18y2z+9yz2=9y(y15x2-6015(x2)(x-2)15x2-60=15(x2-4)15(x+2)(x-2)ax4-8ax2+15aa(x2-3)(x2-)ax4-8ax2+15a=a(x4-8x2+15)15*1 = 153*5=15 3+5=8x4-8x2+15=x4-5x2-3x2+15x2(x2-5)-3(x2-5)=(x2-3)(x2-5)a(x2-3)(x2-5)zt^  DDD2  DDD2  DDD2  D\D2ACT POLY COMP[@PP\ ڧ[@P\ ڧ[ڧڧzڧڧSH<[H10RA?h(p+ZLɍR LͲɊRR% QLܤͲ Z@ -^ ş\[Z QY\[Z8`l6Lş_Ȍb_Ͳ] )Y h( ֭  D\D2IND G.C.F.e33y-5x2y(4xy2)=-20x3y3-5x2y(-6y)=30x2y2-15x3y-20x3y3+30x2y25.2c2(.3-1.2c+c2)1.56c-6.24c3+5.2c45.2c2(.3)=1.56c25.2c2(-1.2c)=-6.24c35.2c2(c2)=5.2c41.56c2+6.24c3+5.2c4x(14)= 112x13x3-16x2+ 112x-6.1y(3-.2y-.1y2)-18.3y+1.22y2+.61y3-6.1y(3)=-18.3y-6.1y(-.2y)=1.22y2-6.1y(-.1y2)=.61y3-18.3y+1.22y2+.61y3-5x2y(3x+4xy2-6y)-15x3y-20x3y3+30x2y2-5x2y(3x)=-15x2m2n32n2(mn2)=2mn42mn3-2m2n3+2mn43xy(x2-2y2)3x3y-6xy33xy(x2)=3x3y3xy(-2y2)=-6xy33x3y-6xy313x(x2-12x+14)13x3-16x2+112x13x(x2)=13x313x(-12x)=-16x213-4rs)=-16r3s24r2s(3)=12r2s12r4s3-16r3s2+12r2s-9z(-3+8z-9z2)27z72z2+81z3-9z(-3)=27z-9z(8z)=-72z2-9z(-9z2)=81z327z-72z2+81z32n2(mn-m2n+mn2)2mn3-2m2n3+2mn2n2(mn)=2mn32n2(-m2n)=-a2(2a+5)2a+5a2a2(2a)=2a3a2(5)+5a22a3+5a2-x2(3x2-2x4)3x4+2x6-x2(3x2)=-3x4-x2(-2x4)=2x6-3x4+2x64r2s(3r2s2-4rs+3)12r4s3-16r3s2+12rs4r2s(3r2s2)=12r4s34r2s(