Factoring Polynomials

Difference of Squares

100

a⁵b - 64ab  

ab(a² + 8)(a² - 8)

200

10x⁵y - 40xy³

10xy(x² - 2y)(x² + 2y)

300

3n⁴ -147

3(n² + 7)(n² - 7)

400

32c⁵d - 162cd³

2cd(4c² - 9d)(4c² + 9d)

Sum and Difference of Cubes

100

250m³ + 54

2(5m + 3)(25m² - 15m + 9)

200

64a³ - 343b³

(4a -7b)(16a² + 28ab + 49b²⁾

300

648w + 1029 w⁴

3w(6 + 7w)(36 -42w +49w²)

400

216pq - p⁷q

pq(6 - p²)(36 + 6p² + p⁴)

Trinomials a = 1 a > 1

100

4w⁴ + 16w² +15

(2w² + 5)(2w² + 3)

200

k⁴ - 10k² - 39

(k² - 13)(k² + 13)

300

3x⁴ - 8x² + 5

(3x² - 5)(x² - 1)

400

x³ - x² - 20x

x(x - 5)(x +4)

Grouping

100

2n³ + 7n² - 2n - 7

(n + 1)(n - 1)(2n + 7)

200

n³ + 2n² - 36n -72

(n + 6)(n - 6)(n + 2)

300

8x³ - 10x² + 28x - 35

(2x² + 7)(4x - 5)

400

x³ - 5x² - x + 5

(x + 1)(x - 1)(x - 5)

Polynomial Equations

100

x³ + 18x = 0

x = {0, +- 3i square root 2}

200

2x⁴ = 50 

x = {0, +- i square root 5, + - square root 5}

300

2x⁴ - 48x² = 0

x = {0, +-2 square roots of 6}

400

25x³ = 64x

x = {0, 8/5, -8/5}