Factoring Polynomials Review

Sum of Cubes

100

Factor: 

a³ + 27

(a + 3)(a² -3a +9)

200

Factor: 

2c³+16

2(c+2)(c²-2c+4)

300

Factor:

125c⁴ + cd³

c(5c + d)(25c² -5cd + d²)

400

Factor:

54x³ + 250y³

2(3x + 5y)(9x² - 15xy + 25y²)

500

Factor:

10x²y² + 80x²y⁵

10x²y²(1+2y)(1-2y+4y²)

Difference of Cubes

100

Factor: 

m³ - 64

(m - 4)(m² + 4m +16)

200

Factor: 

27x³ - 8

(3x - 2) (9x² +6x +4)

300

Factor:

x³y² - 343y⁵

y² (x - 7y) (x² + 7xy + 49y²)

400

Factor:

27w⁵ - w²

w²(3w-1)(9w^w+3w+1)

500

Factor: 

p⁶q⁴ - q⁷

q⁴ (p² - q)(p⁴ + p²q + q²)

Difference of Squares

100

Factor:

a² - 4

(a-2)(a+2)

200

Factor: 

36x² - 9

(6x-3)(6x+3)

300

Factor:

x²+4

PRIME (not a difference of squares!)

400

Factor:

x⁴ - 81

(x-3)(x+3)(x²+9)

500

Factor: 

81u⁴ - 16s⁴

(3u-2s)(3u+2s)(9u²+4s²)

Grouping

100

Factor: 

x³+5x²+3x+15

(x+5)(x²+3)

200

Factor: 

a³ + 2a² - 9a - 18

(a + 2)(a-3)(a+3)

300

Factor: 

2w³ + 3w² - 6w - 9

(2w + 3)(w² - 3)

400

Factor: 

p⁵ - 6p³ - 2p² + 12

(p² - 6)(p³ - 2)

500

Factor: 

8x⁷+x⁴-128x³-16

(2x+1)(4x²-2x+1)(x-2)(x+2)(x²+4)

Trinomial

100

Factor: 

x² - 7x - 30

(x - 10)(x + 3)

200

Factor: 

4a² - 4a + 1

(2a - 1)(2a - 1)

300

Factor: 

9m² + 3m - 2

(3m - 1)(3m + 2)

400

Factor: 

x⁴+5x²+6

(x²+3)(x²+2)

500

Factor:

4x⁴+15x²-4

(2x+1)(2x-1)(x²+4)