Factoring and Solving Higher Degree Polynomials

Honors Math III Name___________________________________ ID: 1 ©Q k2^0H1r5s eKruEtBaC mSOoLf[tSwsaGrueC ^LpLKCM.C r eAolBlw nrRiNg[hYtQsx eruebsxeXrGvleydt. Factoring and Solving Higher Degree Polynomials Date________________ Period____ Use Synthetic Division. n 4 - 5n 3 - 16n 2 + 21n - 9 1) n+3 2) (a 3 + 2a 2 - 56a + 48) ¸ (a - 6) 3) (v 3 - 3v 2 - 35v + 25) ¸ (v + 5) 4) (6n 3 + 17n 2 + 5n - 10) ¸ (n + 2) Use Synthetic Substitution (Remainder Theorem) to evaluate each function at the given value. 5) f (a) = a 3 - 4a 2 + 8a - 22 at a = 3 6) f ( x) = 2x 4 + 18x 3 + 38x 2 + 8x - 16 at x = -6 7) f ( x) = x 3 - 9x 2 + 16x + 6 at x = 3 8) f ( x) = x 4 + x 3 - 21x 2 + 9x - 25 at x = 4 Factor each and find all roots. 9) x 4 - 9 = 0 10) x 4 + 8x 2 - 9 = 0 11) x 3 - 3x 2 - 2x + 6 = 0 12) x 3 - 4x 2 - x + 4 = 0 13) x 4 + 7x 2 + 6 = 0 14) x 4 + 10x 2 + 25 = 0 Worksheet by Kuta Software LLC ©A m2k0k1T5c iKzuwt^a[ BSXoWfLtIwNa\rseu wLCLzCH.k L uAylclR `rEiXgPhutvsy orzefsqeGrSvpeVd^.^ C UMRaqdmeT YwUiptwhe EI]nhfSiYnYiUtfeH CAKlngYeSbSrua_ s2q. Honors Math III Name___________________________________ ID: 1 ©R [2\0z1R5m _KKuatea` cSooRfUtwwGaXrYep pLEL_CX.C R CAflwln Erdiegghntas` ErueesXe\r^vseYd^. Factoring and Solving Higher Degree Polynomials Date________________ Period____ Use Synthetic Division. n 4 - 5n 3 - 16n 2 + 21n - 9 1) n+3 2) (a 3 + 2a 2 - 56a + 48) ¸ (a - 6) a 2 + 8a - 8 n 3 - 8n 2 + 8n - 3 3) (v 3 - 3v 2 - 35v + 25) ¸ (v + 5) v 2 - 8v + 5 4) (6n 3 + 17n 2 + 5n - 10) ¸ (n + 2) 6n 2 + 5n - 5 Use Synthetic Substitution (Remainder Theorem) to evaluate each function at the given value. 5) f (a) = a 3 - 4a 2 + 8a - 22 at a = 3 -7 6) f ( x) = 2x 4 + 18x 3 + 38x 2 + 8x - 16 at x = -6 8 7) f ( x) = x 3 - 9x 2 + 16x + 6 at x = 3 0 8) f ( x) = x 4 + x 3 - 21x 2 + 9x - 25 at x = 4 -5 Factor each and find all roots. 9) x 4 - 9 = 0 Factors to: ( x 2 - 3)( x 2 + 3) = 0 Roots: { 3, - 3, i 3, -i 3 } 11) x 3 - 3x 2 - 2x + 6 = 0 Factors to: ( x - 3)( x 2 - 2) = 0 Roots: {3, 2, - 2 } 13) x 4 + 7x 2 + 6 = 0 Factors to: ( x 2 + 1)( x 2 + 6) = 0 Roots: {i, -i, i 6, -i 6 } 10) x 4 + 8x 2 - 9 = 0 Factors to: ( x - 1)( x + 1)( x 2 + 9) = 0 Roots: {1, -1, 3i, -3i} 12) x 3 - 4x 2 - x + 4 = 0 Factors to: ( x - 4)( x - 1)( x + 1) = 0 Roots: {4, 1, -1} 14) x 4 + 10x 2 + 25 = 0 2 Factors to: ( x 2 + 5) = 0 Roots: {i 5 mult. 2, -i 5 mult. 2} Worksheet by Kuta Software LLC ©U W2b0F1[5r vKruDtAaC GS\opfGtrwuaArAey rLoLGCJ.i Q GAgl^lW LrIiWgYhDtgsS SrgeXsNeHrPvreEdB.U y TMraQdceL owIiqtChT _IxnEfaipnWicteez FAClGgreGbEroaT g2t.