Infinite Algebra 2 - Factoring and Solving Higher Degree ...

Honors Math III

Name___________________________________ ID: 1

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Factoring and Solving Higher Degree Polynomials Date________________ Period____

Use Synthetic Division.

n4 - 5n3 - 16n2 + 21n - 9 1)

n + 3

2) (a3 + 2a2 - 56a + 48) ? (a - 6)

3) (v3 - 3v2 - 35v + 25) ? (v + 5)

4) (6n3 + 17n2 + 5n - 10) ? (n + 2)

Use Synthetic Substitution (Remainder Theorem) to evaluate each function at the given value.

5) f (a) = a3 - 4a2 + 8a - 22 at a = 3

6) f (x) = 2x4 + 18x3 + 38x2 + 8x - 16 at x = -6

7) f (x) = x3 - 9x2 + 16x + 6 at x = 3

8) f (x) = x4 + x3 - 21x2 + 9x - 25 at x = 4

Factor each and find all roots. 9) x4 - 9 = 0

10) x4 + 8x2 - 9 = 0

11) x3 - 3x2 - 2x + 6 = 0

12) x3 - 4x2 - x + 4 = 0

13) x4 + 7x2 + 6 = 0

14) x4 + 10x2 + 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.

n4 - 5n3 - 16n2 + 21n - 9 1)

n + 3 n3 - 8n2 + 8n - 3

2) (a3 + 2a2 - 56a + 48) ? (a - 6)

a2 + 8a - 8

3) (v3 - 3v2 - 35v + 25) ? (v + 5)

v2 - 8v + 5

4) (6n3 + 17n2 + 5n - 10) ? (n + 2)

6n2 + 5n - 5

Use Synthetic Substitution (Remainder Theorem) to evaluate each function at the given value.

5) f (a) = a3 - 4a2 + 8a - 22 at a = 3

-7

6) f (x) = 2x4 + 18x3 + 38x2 + 8x - 16 at x = -6

8

7) f (x) = x3 - 9x2 + 16x + 6 at x = 3

0 Factor each and find all roots.

8) f (x) = x4 + x3 - 21x2 + 9x - 25 at x = 4

-5

9) x4 - 9 = 0

10) x4 + 8x2 - 9 = 0

Factors to: (x2 - 3)(x2 + 3) = 0

Roots: { 3, - 3, i 3, -i 3}

Factors to: (x - 1)(x + 1)(x2 + 9) = 0 Roots: {1, -1, 3i, -3i}

11) x3 - 3x2 - 2x + 6 = 0

Factors to: (x - 3)(x2 - 2) = 0

Roots: {3, 2, - 2}

12) x3 - 4x2 - x + 4 = 0

Factors to: (x - 4)(x - 1)(x + 1) = 0 Roots: {4, 1, -1}

13) x4 + 7x2 + 6 = 0

Factors to: (x2 + 1)(x2 + 6) = 0

Roots: {i, -i, i 6, -i 6}

14) x4 + 10x2 + 25 = 0

Factors to: (x2 + 5)2 = 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.

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