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Algebra 2 Name___________________________________ ID: 1 ©S t2E0c1E5W mKBuntqaH OSuoIfPtpw[asrheK ELdLyCS.m a LAwl_ls JrdiYgWhPtssJ ]rAezsYedravKeXdR. Assignment Date________________ Period____ State the possible rational zeros for each function. Then factor each and find all rational zeros. 1) f ( x) = 2 x 3 - 3 x 2 - 3 x + 2 2) f ( x) = 2 x 3 - 6 x 2 - 45 x - 27 3) f ( x) = 2 x 3 - 5 x 2 + 4 x - 1 4) f ( x) = 3 x 3 - 25 x 2 - 44 x + 10 Worksheet by Kuta Software LLC -1- ©R a2h0Y1_5i zKuu_tia] sSBoRfctOw`ayrCel LLfLGC_.y F zAelIlt DrDixgShbtJsY JrUeNsAeirYvLe^dg.v ^ PMqaKd`eb qw_iut_hO WI\nLfKignWiitUe_ kAJlTgie^bLrBaw E2b. 5) f ( x) = 2 x 3 + x 2 - 2 x - 1 6) f ( x) = 5 x 3 + 31 x 2 + 31 x + 5 7) f ( x) = 2 x 3 - 9 x 2 + x + 18 8) f ( x) = 5 x 3 - 31 x 2 + 31 x - 5 Worksheet by Kuta Software LLC -2- ©q m2j0K1n5P DK_uKtRag eSfoRfEtfw[aprhe_ SLbLgCw.S h LAalbl] OreiYgehatDsS MrzeYsEeKrqv^eLdf.p M YMHaadOeY `wUiftChJ XIQnWfmiInNietkeJ GAtl\gfeBbnruav w2B. 9) f ( x) = x 3 + 11 x 2 + 13 x - 10 10) f ( x) = 2 x 3 + 14 x 2 + 21 x - 9 11) f ( x) = 4 x 4 + 4 x 3 - x 2 - x 12) f ( x) = x 4 + 6 x 3 - 7 x 2 - 18 x Worksheet by Kuta Software LLC -3- ©i C2z0r1P5D jKbuutNaI BSLoof^tLwlavrue_ MLXLtCC.j G cAplHlz brNiUgDhDtBsj vrveksDeOrXv_eXdx.v A aMbaudaew twCiItGh^ sIGnSfuiLnpiqtceu aApl^gFeobfrlaz F2H. Answers to Assignment (ID: 1) 1) Possible rational zeros: ± 1, ± 2, ± 2) Possible rational zeros: 1 2 Factors to: f ( x) = (2 x - 1)( x - 2)( x + 1) { } 1 Rational zeros: , 2, -1 2 3) Possible rational zeros: ± 1, ± 1 2 1 3 9 27 ± 1, ± 3, ± 9, ± 27, ± , ± , ± , ± 2 2 2 2 Factors to: f ( x) = ( x + 3)(2 x 2 - 12 x - 9) Rational zeros: {-3} 4) Possible rational zeros: 1 2 5 10 ± 1, ± 2, ± 5, ± 10, ± , ± , ± , ± 3 3 3 3 Factors to: f ( x) = ( x - 1) 2(2 x - 1) { 1 Rational zeros: 1 mult. 2, 2 Factors to: f ( x) = (3 x + 5)( x 2 - 10 x + 2) } 5) Possible rational zeros: ± 1, ± { } Rational zeros: 1 2 6) Possible rational zeros: ± 1, ± 5, ± Factors to: f ( x) = (2 x + 1)( x + 1)( x - 1) { 1 2 Rational zeros: - , -1, 1 { Factors to: f ( x) = ( x - 2)(2 x - 5 x - 9) Rational zeros: {2} 9) Possible rational zeros: ± 1, ± 2, ± 5, ± 10 Factors to: f ( x) = ( x + 2)( x 2 + 9 x - 5) Rational zeros: {-2} 1 2 1 4 Rational zeros: { } 1 , 1, 5 5 10) Possible rational zeros: 1 3 9 ± 1, ± 3, ± 9, ± , ± , ± 2 2 2 Factors to: f ( x) = ( x + 3)(2 x 2 + 8 x - 3) Rational zeros: {-3} 12) Possible rational zeros: 0, ± 1, ± 2, ± 3, ± 6, ± 9, ± 18 Factors to: f ( x) = x( x - 2)( x 2 + 8 x + 9) Rational zeros: {0, 2} Factors to: f ( x) = x( x + 1)(2 x + 1)(2 x - 1) 1 1 2 2 1 5 Factors to: f ( x) = (5 x - 1)( x - 1)( x - 5) 2 11) Possible rational zeros: 0, ± 1, ± , ± } 8) Possible rational zeros: ± 1, ± 5, ± 1 3 9 ± 1, ± 2, ± 3, ± 6, ± 9, ± 18, ± , ± , ± 2 2 2 { 1 5 Rational zeros: -5, - , -1 7) Possible rational zeros: 1 5 Factors to: f ( x) = ( x + 5)(5 x + 1)( x + 1) } Rational zeros: 0, -1, - , 5 3 } Worksheet by Kuta Software LLC -4- ©z V2n0b1P5C cKdumtLa^ qSHoLfwtlwLaarjei MLbLaCd.s S \AflGlx sr]ilgchYtYsR ersehsxeyrVvae]dW.H [ AM`aldiew jw\iztghr \INnoftiJnZiitZek BAIl^gCe[burLaq I2L.