Factoring by using theGreatest Common Factor (GCF)

Lesson 2.5

Page 77

Recall finding the Prime Factorization of a number

1.

2.

20 5 4 5 2 2

2150x 15 10 x x 5 3 5 2 x x 2 3 5 5 x x

2 2 5

Finding the GCF

The GCF is the product of the common factors in each term of the polynomial.

4 2Factor the GCF out of 14 21 .x x

414 2 7 xxx xx 221 3 7 xx x

Then use the distributive property to factor the GCF out of the

polynomial.27 GCF o xr 7x x

2 2 24 7 (1 3)14 22x x xx

When you factor the GCF out of a polynomial,

what remains in each term goes in parentheses.

Find the GCF of the following:

1.

2.

3.

315 , 20xx 5x3 2 2 28 , 12abc a b c

24abc2 4 36 , 15x y x yz

23x y

Factor out the greatest common monomial factor.

The GCF is 8.

8 8x y

8( )x y

Factor out the greatest commonmonomial factor.

4 214 35a a2The GCF is 7 .a

2 27 (2 5)a a

Try the following.

3

5 4

2

1. 4 6

2. 44 33

3. 6 14

4. 15 5

r rs

m mn

y y

a b ab

Answers:

1. 2 (2 3 )r s22. 11 (4 3 )m m n

43. 2 (3 7)y y

4. 5 (3 1)ab a

Homework Assignment:

Page 79 # 13 – 21 all

Page 80 # 10 – 18 all