Factoring by using the Greatest Common Factor (GCF) Lesson 2.5 Page 77
Jun 19, 2015
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