Factoring Polynomials

Factor by GCF

100

Factor out the GCF.

12x + 21

3 ( 4x + 7 )

200

Factor out the GCF.

14x^2-35

7 (2x^2-5)

300

Factor out the GCF.

-15x^4+24x

-3x (5x^3-8)

or

3x(-5x^3+8)

400

Factor out the GCF.

4x^7-16x^5+24x^3

4x^3 (x^4-4x^2+6)

500

Factor out the GCF.

12x^6+6x^5-36x^3+24x^2-18x

6x(2x^5+x^4-6x^2+4x-3)

Difference of Squares

100

Factor this binomial.

x^2 - 9

(x + 3) (x - 3)

200

Factor this binomial.

x^2 - 121

(x + 11) ( x-11)

300

Factor this binomial.

25x^2- 81

(5x + 9) (5x-9)

400

Factor this binomial.

36x^2-16

(6x+4)(6x-4)

500

Factor this binomial.

32x^2-50

2 (4x+5)(4x-5)

Sum/Difference of Cubes

100

Factor this binomial.

x^3-8

(x-2)(x^2+2x+4)

200

Factor this binomial.

x^3+27

(x+3)(x^2-3x+9)

300

Factor this binomial.

27x^3-8

(3x-2)(9x^2+6x+4)

400

Factor this binomial.

64x^3+125

(4x+5)(16x^2-20x+25)

500

Factor this binomial.

16x^3-54

2 (2x-3)(4x^2+6x+9)

Factoring Trinomials

100

Factor this trinomial.

x^2+9x+14

(x+7)(x+2)

200

Factor this trinomial.

x^2+x-30

(x+6)(x-5)

300

Factor this trinomial.

3x^2+5x+2

(3x+2)(x+1)

400

Factor this trinomial.

6x^2-5x-14

(6x+7)(x-2)

500

Factor this trinomial.

9x^3-33x^2+18x

3x(3x-2)(x-3)

Factor by Grouping

100

Factor this quadrinomial.

x^3-2x^2+x-2

(x^2+1)(x-2)

200

Factor this quadrinomial.

4x^3-5x^2+64x-80

(x^2+16)(4x-5)

300

Factor this quadrinomial.

x^3-2x^2-x+2

(x+1)(x-1)(x-2)

400

Factor this quadrinomial.

16x^3+16x^2-9x-9

(4x+3)(4x-3)(x+1)

500

Factor this quadrinomial.

4x^3+4x^2-100x-100

4(x+5)(x-5)(x+1)