Factoring Polynomials

Grouping

100

35n²+5n²-7n-1

(5n²-1)(7n+1)

200

x⁶-3x⁴-25x²+75

(x²-3)(x⁴-25)

300

8x³-x²+56x-7

(x²+7)(8x-1)

400

21p³+28p²-9p-12

(7p²-3)(3p+4)

500

x⁶+3x⁴-x²-3

(x⁴-1)(x²+3) or (x² - 1)(x² + 1)(x² + 3)

Three Terms

100

n⁴-8n²+16

(n² - 4)² or (n² - 4)(n² - 4)

200

x⁴-10x²+25

(x² - 5)(x² - 5) or (x² - 5)²

300

9n²+12n+4

(3n+2)²

400

5k⁴+4k²-1

(5k²-1)(k²+1)

500

7k²-13k-2

(7k+1)(k-2)

Difference of Cubes

100

x³-8

(x-2)(x²+2x+4)

200

x³-27

(x-3)(x²+3x+9)

300

54-2x³

2(3-x)(9+3x+x²)

400

1-216u³

(1-6u)(1+6u+36u²)

500

8x⁶-x³

x³(2x-1)(4x²+2x+1)

Difference of Squares

100

9k²-1

(3k+1)(3k-1)

200

16v²-25

(4v+5)(4v-5)

300

16m²-9

(4m+3)(4m-3)

400

18v²-32

2(3v+4)(3v-4)

500

48n²-27

3(4n+3)(4n-3)

Sum of Cubes

100

216x³+125

(6x+5)(36x²-30x+25)

200

125u³+1

(5u+1)(25u²-5u+1)

300

64+a³

(4+a)(16-4a+a²)

400

125a³+216

(5a+6)(25a²-30a+36)

500

256x+500x⁴

4x(4+5x)(16-20x+25x²)