FACTORING POLYNOMIALS

Factoring trinomials

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- harder

100

Factor into two binomials: 12x²+36x+27

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

200

Factor into two binomials: -2n²-12n-10

-2(n+1)(n+5)

300

Factor into two binomials: 2x²-12x-54

2(x+3)(x-9)

400

Factor into two binomials: x²-24x-25 + (x-25)

(x-25)[(x+1) + 1]

500

Factor into two binomials: 2x²-12x+10

(2x-2)(x-5)

GCF

100

Find the GCF: 3x², 12x

3x

200

Find the GCF: 4x³, 10x²

2x²

300

Find the GCF: 2x⁵, 9x⁴

x⁴

400

Find the GCF: 18x³, 32x²+6x

2x

500

Find the GCF: 12m⁴n³, 6m³n², 24m²n⁴

6m²n²

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:  x² - 196

(x+14)(x-14)

200

Factor:  81x⁴ +18x² + 1

(9x² + 1)² 

300

Factor:  20x² - 125y⁴ 

5(2x-5y²)(2x+5y²)

400

Factor:  81x⁴ - 1 (be careful)

(9x² +1)(3x+1)(3x-1)

500

Factor:  81x⁴ -18x² + 1

(3x+1)²(3x-1)²