FACTORING POLYNOMIALS

Factoring Trinomials 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 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

Factor into two binomials: 2x²-12x+10

(2x-2)(x-5)

Factor by Grouping

100

Factor by Grouping:        5a³ - 5a² + 2a -2

(5a + 2)(a-1)

200

Factor by Grouping:     12x³ + 3x² + 8x + 2

(3x² + 2)(4x + 1)

300

   Factor by grouping:             2xy + 5x + 14y + 35

(x+7)(2y+5)

400

   Factor by grouping:             3v³ + 5v² + 3v + 5

(v² + 1)(3v + 5)

500

    Factor by grouping:              8g³ + 20g² + 6g + 15

(4g² + 3)(2v+5)

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)

Special Cases

100

Factor: 9x² - 49y²

(3x + 7y)(3x - 7y)

200

Factor: 100n² - 30n + 9

(10n - 3)²

300

Factor: 81y² + 1

Not a Difference of Squares. Prime

400

Factor: -16 + x²

(x +4)(x - 4)

500

Factor: 25x² +110x + 121

(5x + 11)(5x - 11)