Factoring

Binomials

100

Factor completely.

x² - x

x(x - 1)

200

Factor completely.

5x² + 15x

5x(x + 3)

300

Solve by factoring.

4n² - 25 = 0

n = 5/2 ; -5/2

400

Solve by factoring.

63x² - 700 = 0

x = 10/3 ; -10/3

500

Factor completely.

180x² - 245

5(6x + 7)(6x - 7)

Trinomials

100

Solve.

k² + k - 6 = 0

k = -3 ; 2

200

Solve by factoring.

4a² + 24a + 32 = 0

a = -4 ; -2

300

Solve by factoring. 

5r² - 21r + 18 = 0

r = 6/5 ; 3

400

Solve by factoring. 

18x² + 69x - 12 = 0

x = 1/6 ; -4 

500

Solve by factoring.

15x² - 10x - 12 = -7

x = -1/3 ; 1

Polynomials

100

Factor completely. 

x³ - 3x² + x - 3

(x² + 1)(x - 3)

200

Factor completely.

6p³ - 9p² + 4p - 6

(3p² + 2)(2p - 3)

300

Factor completely.

14r³ + 35r² - 4r - 10

(7r² - 2)(2r + 5)

400

Factor completely.

6n³ + 3n² - 12n - 6

3(n² - 2)(2n+1)

500

Factor completely.

9aw - 3af - 9xw + 3xf

3(a - x)(3w - f)

GCF

100

What is the greatest common factor between 4, 8, and 12?

4

200

What is the greatest common factor between 45 and 54.

9

300

What is the greatest common factor between 14, 28, and 105

7

400

What is the greatest common factor between 12x⁵ and 48x³?

12x³

500

What is the greatest common factor between 108x¹⁸y⁵z⁷ and 63x⁹yz⁶?

9x⁹yz⁶