FACTORING POLYNOMIALS

Factor by GCF

100

Factor by GCF: 14n²+10n

2n(7n+5)

200

Factor by GCF: 18x³-6x

6x(3x²-1)

300

Factor by GCF: 8-4a²

4(2-a²)

400

Factor by GCF: 4x⁴+16x³-8x²

4x²(x²+4x-2)

500

Factor by GCF: 10a³b⁴-6a²b⁶

2a²b⁴(5a³-3b²)

Factor Difference of Squares

100

Factor Completely: m²-144

(m-12)(m+12)

200

Factor Completely: 16x²-121

(4x+11)(4x-11)

300

Factor Completely: 100 - 9y²

(10+3y)(10-3y)

400

Factor Completely: x⁴-y⁴

(x²+y²)(x+y)(x-y)

Acceptable Answer: (x²+y²)(x²-y²)

500

Factor Completely: 81y⁴-1

(9y²+1)(3y+1)(3y-1)

Acceptable Answer: (9y²+1)(9y²-1)

Factoring Trinomials

100

Factor into two binomials: x²+8x+12

(x+6)(x+2)

200

Factor into two binomials: x²-x-56

(x-8)(x+7)

300

Factor into two binomials: x²+5x-24

(x+8)(x-3)

400

Factor into two binomials: 5n²+26n+5

(5n+1)(n+5)

500

Factor into two binomials: 3x²-10x+7

(3x-7)(x-1)

Factoring By Grouping

100

Factor Completely: x³+3x²-5x-15

(x+3)(x²-5)

200

Factor Completely: 14x³-7x²+2xy-y

(2x-1)(7x²+y)

300

Factor Completely: x³+4x²+2x+8

(x+4)(x²+2)

400

Factor Completely: 2x³+x²y-6xy²-3y³

(2x+y)(x²-3y²)

500

Factor Completely: 9x³+9x²y-x-y

(x+y)(3x+1)(3x-1)

Acceptable answer: (x+y)(9x²-1)

Mixed Factoring

100

Factor Completely: x³-10x²+21x

x(x-7)(x-3)

200

Factor Completely: 5a²+10ab-3a-6b

(a+2b)(5a-3)

300

Factor Completely: 64x²-4y²

4(4x+y)(4x-y)

400

Factor Completely: 75x²-30x+3

3(5x-1)²

500

Factor completely: 48x⁵-3x

3x(4x² + 1)(2x+1)(2x-1)