FACTORING POLYNOMIALS

Factoring Trinomials when a=1

100

Factor into two binomials: x²+8x+12

(x+6)(x+2)

200

Factor into two binomials: m²-11m+18

(m-9)(m-2)

300

Factor into two binomials: x²+5x-24

(x+8)(x-3)

400

Factor into two binomials: y²-6y-7

(y-7)(y+1)

500

Factor into two binomials: x²-x-56

(x-8)(x+7)

Factoring Trinomials when a > 1

100

Factor into two binomials: 2x²+7x+3

(2x+1)(x+3)

200

Factor into two binomials: 5n²+26n+5

(5n+1)(n+5)

300

Factor into two binomials: 3x²-10x+7

(3x-7)(x-1)

400

Factor into two binomials: 7x²-36x+5

(7x-1)(x-5)

500

2x²-12x+10

2(x-1)(x-5)

Factor by Grouping

100

3x(x+2) + 4(x+2)

(3x+4)(x+2)

200

4x³ + 28x² + 7x + 49

(4x² + 7)(x + 7)

300

10xy + 3y + 20ax + 6a

(y + 2a)(10x + 3)

400

14bx² - 7x³ - 4b + 2x

(7x² - 2)(2b - x)

500

10ax + 5bx - 8ay - 4by

(2a + b)(5x - 4y)

Factor by GCF

100

14n²+10n

2n(7n+5)

200

18x³ - 6x

6x(3x²-1)

300

8 - 4a²

4(2-a²)

400

4x⁴ + 16x³ - 8x²

4x²(x²+4x-2)

500

10a³b⁴ - 6a²b⁶

2a²b⁴(5a-3b²)

Perfect Squares

100

x² - 8x + 16

(x - 4)(x - 4) or (x - 4)²

200

x² - 25

(x+5)(x-5)

300

2x² - 32

2(x + 4)(x - 4)

400

9x² + 42x + 49

(4x + 5)(4x + 5) or (4x + 5)²

500

2x³ + x² - 18x - 9

(x - 3)(x + 3)(2x + 1)