Factoring Polynomials

GCF

100

2x + 2y

2(x + y)

200

12x²+ 4x³

4x²(3+x)

300

4xy² - 8xy + 2x²y

2xy(2y - 4 + x)

400

4(x + 1) + 7x(x + 1)

(x + 1)(4 + 7x)

500

x^3/2y^3/4 - x^1/2y^5/4

x^1/2y^3/4(x - y^1/2)

Factor by Grouping

100

x³ + 3x² + 4x + 12

(x+3)(x² + 4)

200

2x³ + 6x² + 9x + 27

(x + 3)(2x² + 9)

300

x³ - 5x² - 3x +15

(x-5)(x² -3)

400

8x³ +6x² - 4x - 3

(4x + 3)(2x² - 1)

500

x^3/2 - 2x^1/2 + 2x - 4

(x - 2)(x^1/2 + 2)

Trinomials

100

x² + x - 20

(x + 5)(x - 4)

200

x² + 17x + 52

(x + 13) (x + 4)

300

x² + 10xy - 96y²

(x + 16y)(x - 6y)

400

x² - 68xy² - 288y⁴

(x + 4y²)(x - 72y²)

500

x^4/5 + 10x^2/5 - 56

(x^2/5 +14)(x^2/5 - 4)

Special Cases

100

x² - 25

(x + 5)(x - 5)

200

x² + 36

Prime

300

4x² - 49

(2x + 7)(2x - 7)

400

9x² + 12x + 4

(3x + 2)²

500

100x^2/3 - 60x^1/3 + 9

(10x^1/3 - 3)²

Factor Completely

100

2x² + 6x + 4

2(x + 1)(x + 2)

200

5x²y - 60xy + 135y

5y(x - 9)(x - 3)

300

-4x³ + 24x² - 36x

-4x(x - 3)²

400

18x²y² - 98y²

2y²(3x - 7)(3x + 7)

500

x⁴ - 81

(x² + 9)(x + 3)(x - 3)