FACTORING using GCF and D.O.T.S

GCF Basics

100

6x + 12

6(x + 2)

200

8x + 20

4(2x + 5)

300

12x² + 18x

6x(2x + 3)

400

15a²b + 25ab²

5ab(3a + 5b)  

500

24x³y² − 36x²y³

12x²y²(2x − 3y)

DOTS Basics

100

x² − 9

(x − 3)(x + 3)

200

x² − 25

(x − 5)(x + 5)

300

4x² − 49

(2x − 7)(2x + 7)

400

9a² − 64

(3a − 8)(3a + 8)

500

25x⁴ − 81y²

(5x² − 9y)(5x² + 9y)

Factor using the GCF

100

3x²-12x

3x(x-4)

200

3x+6

3(x+2)

300

4ab-8

4(ab-2)

400

4ab²-12a²b

4ab(b-3a)

500

3x²y²-2xy

xy(3xy-2)

True or False

100

The GCF of 8x and 12x is 4x.

TRUE

Both terms are divisible by 4x.

200

x² − 36 = (x − 6)(x + 6).

TRUE

This is a difference of two squares.

300

12x² + 18x = 6x(2x + 3).

TRUE

400

9x² − 16 = (3x − 4)².

FALSE

The correct factorization is (3x − 4)(3x + 4).

500

The expression x² − 25 can be factored as (x − 5)(x + 5).

TRUE!

This is a difference of two squares.

Factoring the difference of two perfect squares

100

16x² − 1

(4x − 1)(4x + 1)

200

9-x²

(3+x)(3-x)

300

25y²-4

(5y+2)(5y-2)

400

4x²-400

(2x + 20) (2x - 20)

500

x²+100

Can not be factored because of the plus sign.