Factoring Polynomials

Factor the GCF

100

FIND THE GCF:

18x³  and 28x⁵

2x³

200

FIND THE GCF:

30a⁴b  and 48a³b³

6a³b

300

Factor out the GCF:

12a⁴  -  4a³ + 16a²

4a²(3a² - a + 4)

400

Factor out the GCF:

15a⁵ + 30a⁴ - 45a²

15a²(3a³ + 2a² -3)

500

Factor out the GCF:

3x³y - 3x²y² + 12x²y³

3x²y(x - y + 4y²)

Factoring Trinomials

100

FACTOR: x² + 11x +30

(x + 5)(x + 6)

200

FACTOR: x² - 10x - 24

(x + 2)(x - 12)

300

FACTOR: x² - 7x + 12

(x - 3)(x - 4)

400

FACTOR: 2x² + 17x + 8

HINT: Split the middle on this one.

(2x + 1)(x + 8)

500

FACTOR: 6x² + 7x + 2

Hint: Split the middle term.

(3x + 2)(2x + 1)

Factoring using Difference of Squares

100

FACTOR: x² - 100

(x + 10)(x - 10)

200

FACTOR: 25x² - 36

(5x + 6)(5x - 6)

300

FACTOR: 100x² - 121y²

(10x + 11y)(10x - 11y)

400

289x² - 9y²

(17x + 3y)(17x - 3y)

500

676x² - 961y²

(26x + 31y)(26x - 31y)

Factor by grouping (4 terms)

100

Factor: x³ + 10x² + x + 10

(x²+10)(x + 1)

200

Factor: x³ - 2x² - 2x +4

(x² - 2)(x - 2)

300

Factor: 6x³ + 3x² - 8x - 4

(2x + 1)(3x² - 4)

400

FACTOR: 20x³ - 5x² + 8x - 2

(5x² + 2)(4x - 1)

500

Factor: 3x³ - 2x² - 12x + 8

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

Solving Equations by factoring

100

SOLVE: (x + 5)(x - 8) = 0

x = -5, x = 8

200

SOLVE: (2x + 7)(3x - 12) = 0

x = -3.5 and x = 4

300

FACTOR.  Then solve for x.

x² - x - 12 = 0

x = -3, x = 4

400

FACTOR.  THEN SOLVE FOR X.

x² - 196 = 0

x = 14, x = -14

500

FACTOR.  THEN SOLVE FOR X.

x² + 8x - 20 = 0

x = -10, x = 2