Factor problems 1-4 by finding the GCF.

1.4x³- 12x²+ 4x

A.4x(x2- 3x+ 1)

B.4x(4x2- 3x+ 1)

C.4x(4x2- 3x- 1)

D.4x(x2- 6x+ 1)

E.2x(2x2- 6x+ 2)

F.This polynomial cannot be factored using the GCF method.

2. 9x⁴+ 4x³- 27x²+ 12x

A.x(9x3+ 4x2+ 27x+ 12)

B.x(9x3+ 4x2- 27x + 12)

C.x(9x4+ 4x3- 27x2+ 12x)

D.x4(9x3+ 4x2+ 27x+ 12)

E.x(9x4+ 4x3- 27x2+ 12x)

F.This polynomial cannot be factored using the GCF method.

3.x²- 3x + 4

A.x(x - 3)

B.x(x + 3)

C.x(x - 1)

D.x(x - 7)

E.x(x + 7)

F.This polynomial cannot be factored using the GCF method.

4.17x⁵+ 51x²- 34

A.17x5+ 3x2+ 2

B.17(x3+ 3x2+ 2)

C.17(x4+ 3x2+ 2)

D.17(x5+ 3x2- 2)

E.x5+ 3x2- 2

F.This polynomial cannot be factored using the GCF method.

Factor problems 5 - 8 by grouping.

5.x²- 2x + 1

A.(x - 1)(x - 1)

B.(x - 1)(x + 1)

C.(x + 1)(x - 1)

D.(x + 1)(x + 1)

E.(x + 2)(x - 1)

F.This polynomial cannot be factored by grouping.

6.x²+ 2x - 15

A.(x - 5)(x - 3)

B.(x + 5)(x + 3)

C.(x + 5)(x - 3)

D.(x - 5)(x + 3)

E.(x + 15)(x - 1)

F.This polynomial cannot be factored by grouping.

7.x²- 3x - 18

A.(x + 3)(x + 6)

B.(x + 3)(x - 6)

C.(x - 3)(x - 6)

D.(x - 3)(x + 6)

E.(-x + 3)(x + 6)

F.This polynomial cannot be factored by grouping.

8.8x²+ 47x + 28

A.This polynomial cannot be factored by grouping.

B.(3x + 7)(5x - 4)

C.(3x - 7)(5x - 4)

D.(3x + 7)(-5x + 4)

E.(-3x + 7)(-5x + 4)

F.(3x + 7)(5x + 4)

Factor problems 9 - 12 by using the difference of squares method.

9.x²- 4

A.This polynomial cannot be factored by using the difference of squares method.

B.(x - 2)(x - 2)

C.(x - 2)(x - 1)

D.(x - 2)(x + 2)

E.(x - 1)(x - 4)

F.(x + 2)(x + 2)

10.x²- 25

A.(-x - 5)(x - 5)

B.This polynomial cannot be factored by using the difference of squares method.

C.(-x + 5)(x + 5)

D.(x - 5)(x + 5)

E.(x + 5)(-x - 5)

F.(x - 5)(x - 5)

11.36x⁴- 4x²

A.(6x2- 2x)(6x2- 2x) = 4x2(3x - 1)(3x - 1)

B.(6x2+ 2x)(6x2+ 2x) = 2x2(3x + 1)(2x + 1)

C.This polynomial cannot be factored by using the difference of squares method.

D.(-6x2- 2x)(-6x2- 2x) = 4x2(-3x - 1)(-3x - 1)

E.(6x2- 2x)(6x2+ 2x) = 4x2(3x - 1)(3x + 1)

F.(-6x2+ 2x)(6x2- 2x) = 2x2(-3x + 1)(3x - 1)

12.x²+ 100

A.(x + 10)(x - 10)

B.(-x + 10)(x - 10)

C.(x + 10)(x + 10)

D.This polynomial cannot be factored by using the difference of squares method.

E.(x - 10)(x - 10)

F.(-x + 10)(-x - 10)

Factor problems 13 - 16 by using the perfect squares method.

13.x²- 14x + 49

A.(-x - 7)(-x - 7)

B.(x + 7)(x - 7)

C.(x + 7)(x + 7)

D.(x - 7)(x + 7)

E.(x - 7)(x - 7)

F.This polynomial cannot be factored by using the perfect squares method.

14.x²+ 18x + 81

A.(x + 9)(x + 9)

B.(-x + 9)(-x + 9)

C.(x - 9)(x - 9)

D.(x + 9)(x - 9)

E.(x - 9)(-x + 9)

F.This polynomial cannot be factored by using the perfect squares method.

15.x²- 3x + 16

A.(x - 4)(x - 4)

B.(x - 4)(x + 4)

C.(x + 4)(x + 4)

D.(x + 4)(x - 4)

E.(-x - 4)(-x - 4)

F.This polynomial cannot be factored by using the perfect squares method.

16.4x⁴- 20x²+ 25

A.(2x2+ 5)(2x2+ 5)

B.(2x2- 5)(2x2+ 5)

C.(-2x2- 5)(-2x2- 5)

D.(2x2- 5)(2x2- 5)

E.(2x2- 5)(-2x2+ 5)

F.This polynomial cannot be factored by using the perfect squares method.

For problems 17 - 20, identify which of the methods from this lesson (GCF, grouping, difference of squares, or perfect squares)couldbe used to factor the polynomial.

17.x²+ 2x + 1

A.This polynomial could be factored by finding the GCF, then by grouping or using the perfect squares method.

B.This polynomial could be factored by using the difference of squares method, perfect squares method, or grouping.

C.This polynomial could be factored only by using the perfect squares method.

D.This polynomial could be factored only by using the difference of squares method.

E.This polynomial could be factored by using grouping or the perfect squares methods.

F.This polynomial cannot be factored by any of the methods used in this lesson.

18.2x³+ 4x²+ 2x

A.This polynomial could be factored by finding the GCF, then by grouping or using the perfect squares method.

B.This polynomial could be factored by using the difference of squares method, perfect squares method, or grouping.

C.This polynomial could be factored only by using the perfect squares method.

D.This polynomial could be factored by using grouping or the perfect squares methods.

E.This polynomial could be factored only by using the difference of squares method.

F.This polynomial cannot be factored by any of the methods used in this lesson.

19.x²- 169

A.This polynomial could be factored by finding the GCF, then by grouping or using the perfect squares method.

B.This polynomial could be factored by using the difference of squares method or grouping.

C.This polynomial could be factored only by using the perfect squares method.

D.This polynomial could be factored by using grouping or the perfect squares methods.

E.This polynomial could be factored only by using the difference of squares method.

F.This polynomial cannot be factored by any of the methods used in this lesson.

20.x²+ 5x - 7

A.This polynomial could be factored by finding the GCF, then by grouping or using the perfect squares method.

B.This polynomial could be factored by using the difference of squares method, perfect squares method, or grouping.

C.This polynomial could be factored only by using the perfect squares method.

D.This polynomial could be factored by using grouping or the perfect squares methods.

E.This polynomial could be factored only by using the difference of squares method.

F.This polynomial cannot be factored by any of the methods used in this lesson.