Factoring Game

Factor by GCF

100

15x + 75

What is 15(x+5)?

200

4x³ + 7xy

What is x(4x² + 7y)?

300

xy + xz + 2x⁵

What is x(y+z+2x⁴)?

400

x⁵ + 2x⁴ + 3x² + 16x; 5x + 3

What is five times the GCF of x⁵ + 2x⁴ + 3x² + 16x plus three?

500

(1/2)x⁷ + (1/4)x⁵ + (1/8)x³ + (1/16)x; x + 1

What is two times the GCF of ((1/2)x⁷ + (1/4)x⁵ + (1/8)x³ + (1/16)x) added by one?

Difference of Squares

100

4x² - 81

What is (2x - 9)(2x + 9)?

200

225z² - 169y²

What is (15z - 13y)(15z + 13y)?

300

121x⁴y² - 81a⁶z⁴

What is (11x²y - 9a³z²)(11x²y + 9a³z²)?

400

x^2y - b^2z

What is (x^y - b^z)(x^y + b^z) when y and z are all positive integers?

500

x^(2y+4) - (4b)^{(2y + 4)}​​​​

What is (x^y+2 + (4b)^y+2)(x^y+2 - (4b)^y+2)?

Factor by grouping

100

x² + 12x + 36

What is (x+6)(x+6) or (x+6)²?

200

x² - 10x + 24

What is (x-6)(x-4)?

300

4z² - 16xz + 15x²

What is (2z - 3x)(2z - 5x)?

400

4b³ + b² + 8b + 2

What is (b² + 2)(4b + 1)?

500

x^2y + x^3y + x^4y + x^5y

What is x^2y(1 + x^2y)(1+x^y)?

Factoring completely (multistep)

100

8x² - 18

What is 2(x+9)(x-9)?

200

25x² - 100y²

What is 25(x-2y)(x+2y)?

300

5x² - 25x - 120

What is 5(x-8)(x+3)?

400

4a² - 20ab + 25b² - 100

What is [(2a - 5b) + 10][(2a - 5b) - 10]?

500

4x² + 12xy + 9y² - 9r² - 24rs - 16s²

What is [(2x+3y) + (3r+4s)][(2x+3y) - (3r+4s)]?