Factoring, Factoring, Factoring!!

Greatest Common Factor

100

Factor: 

3x + 12

3(x + 4)

200

Factor: 

8m + 36n

4(2m + 9n)

300

Factor:

21cd - 3d

3d(7c - 1)

400

Factor:

18a²bc² - 48abc³

6abc²(3a - 8c)

500

Factor:

9r⁸ - 18r²s - 24rs²

3r(3r⁷ - 6rs - 8rs²)

Difference of Squares

100

Factor:

a² - 4

(a+2)(a-2)

200

Factor: 

c² - 100

(c + 10)(c - 10)

300

Factor: 

x² + 25

Prime. 

You cannot factor because this is not a difference of squares problem. 

400

Factor: 

16a² - 121

(4a + 11)(4a - 11)

500

Factor: 

64u² - 36s²

(8u + 6s)(8u - 6s)

Factor Trinomials

100

Factor: 

a2 + 2a + 1

(a + 1)(a + 1)

200

Factor: 

x² - 7x + 12

(x - 3)(x - 4)

300

Factor: 

w² - 6w - 27

(w - 9)(w + 3)

400

Factor: 

p² - 11p + 30

(p - 6)(p - 5)

500

Factor: 

y² - 14y - 51

(y + 3)(y - 17)

Factor Completely

100

Factor: 

2x² + 18x + 40

2(x + 4)(x + 5)

200

Factor: 

3a² + 30a + 72

3(a + 4)(a + 6)

300

Factor: 

6n² - 15n - 9

3(2n + 1)(n - 3)

400

Factor: 

2x² - 32

2(x - 4)(x + 4)

500

Factor: 

3y² + 27

2(y² + 9)

Area and dimensions

100

A rectangle has an area of 2x² + 15x + 28. If its width is x + 4, find the length.

(2x + 7)

200

If the area of a rectangle can be represented by the expression x² - 49, what are the dimensions?

(x + 7)(x - 7)

300

A rectangular backyard has an area of 2x² + 5x + 2. Find its width and length. 

(2x + 1)(x + 2)

400

A baseball diamond has an area of x² + 10x + 25. Find the measure from home plate to first base.

(x + 5)

500

The perimeter of a rectangle is 6x - 10. The length of one side is x + 2. Find the area.

2x² - 3x - 14