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: 

7x² - 36x + 5

(7x - 1)(x - 5)

500

Factor into two binomials: 

3x² - 10x + 7

(3x - 7)(x - 1)

Factoring Binomials

100

Factor into two binomials: 

x² - 36

(x + 6)(x - 6)

200

Factor into two binomials: 

y² - 100

(y + 10)(y - 10)

300

Factor into two binomials: 

m² - 441

(m + 21)(m - 21)

400

Factor into two binomials: 

x⁴ - 4y²

(x² + 2y)(x² - 2y)

500

Factor into two binomials: 

49a² - 81b²

(7a + 9b)(7a - 9b)

Factoring Polynomials with 4 terms

100

Factor by grouping:  

x² + 3x + 2x + 6

(x + 3)(x + 2)

200

Factor by grouping:  

x² + 5x + 4x + 20

(x + 5)(x + 4)

300

Factor by grouping:  

15x³ + 5x² + 3x + 1

(3x + 1)(5x² + 1)

400

Factor by grouping:

x³ + 4x + x² + 4

**hint:  you may have to rearrange the terms

x³ + x² + 4x + 4

(x + 1)(x² + 4)

500

Factor by grouping:  

6aw - 36ak + 6b²w - 36b²k

**hint:  you may have to rearrange the terms

6aw + 6b²w - 36ak - 36b²k

(a + b²)(6w - 36k)

Factoring ANY polynomial

100

Find the GCF of...

3x² and 12x⁴

3x²

200

Find the GCF of...

14x², 49x, and 56

7

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 Completely

100

3x² - 27

3(x² - 9)

3(x + 3)(x - 3)

200

2x³ - 18x

2x(x² - 9)

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

300

2x² - 10x + 12

2(x² - 5x + 6)

2(x - 3)(x - 2)

400

5x²y³ - 180y

5y(x²y² - 36y²)

5y(xy + 6y)(xy - 6y)

500

x³ + 3x² - 4x - 12

(x + 3)(x² - 4)

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