1. Factoring by using the
Greatest Common Factor (GCF)
Lesson 2.5
Page 77

2. Recall finding the Prime Factorization of a number
1.
2.
20 5 4= × 5 2 2= × ×
2
150x 15 10 x x= × × ×
5 3 5 2 x x= × × × × × 2 3 5 5 x x= × × × × ×
2 2 5= × ×

3. Finding the GCF
The GCF is the product of the common
factors in each term of the polynomial.
4 2
Factor the GCF out of 14 21 .x x−
4
14 2 7 xxx xx= × × × × ×
2
21 3 7 xx x= × × ×

4. Then use the distributive property
to factor the GCF out of the
polynomial.
2
7GCF 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.

5. Find the GCF of the following:
1.
2.
3.
3
15 , 20xx 5x
3 2 2 2
8 , 12abc a b c
2
4abc
2 4 3
6 , 15x y x yz
2
3x y

6. Factor out the greatest common
monomial factor.
The GCF is 8.
8 8x y−
8( )x y−

7. Factor out the greatest common
monomial factor.
4 2
14 35a a+
2
The GCF is 7 .a
2 2
7 (2 5)a a +

8. 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
+
−
−
+

9. Answers:
1. 2 (2 3 )r s+
2
2. 11 (4 3 )m m n−
4
3. 2 (3 7)y y −
4. 5 (3 1)ab a +

10. Homework Assignment:
Page 79 # 13 – 21 all
Page 80 # 10 – 18 all