Download Factoring GCF

Objectives
The student will be able to:
Factor using the greatest common
factor (GCF).
Review: What is the GCF of
25a2 and 15a?
5a
Let’s go one step further…
1) FACTOR 25a2 + 15a.
Find the GCF and divide each term
25a2 + 15a = 5a( ___
5a + ___
3 )
25a 2
5a
15a
5a
Check your answer by distributing.
2) Factor
2
18x
-
3
12x .
Find the GCF
6x2
Divide each term by the GCF
18x2 - 12x3 = 6x2( ___
3 - ___
2x )
18 x 2
6x2
12 x 3
6 x2
Check your answer by distributing.
You Try It: Factor 20x2 - 24xy
1.
2.
3.
4.
x(20 – 24y)
2x(10x – 12y)
4(5x2 – 6xy)
4x(5x – 6y)
The GCF of 20 and 24 is 4.
The GCF of x2 and xy is x.
So we can take 4x out of the
expression.
Divide each term by the GCF.
20x2 – 24xy = 4x(5x – 6y)
4x
4x
5) Factor
2
28a
+ 21b -
2
2
35b c
GCF = 7
Divide each term by the GCF
28a2 + 21b - 35b2c2 = 7 ( ___
4a2 + ___
3b - ____
5b2c2 )
28a 2
7
21b
7
35b 2 c 2
7
Check your answer by distributing.
7(4a2 + 3b – 5b2c2)
You Try It:
Factor 16xy2 - 24y2z + 40y2
1.
2.
3.
4.
2y2(8x – 12z + 20)
4y2(4x – 6z + 10)
8y2(2x - 3z + 5)
8xy2z(2 – 3 + 5)
What’s the GCF?
8y2
Divide each term by the
GCF.
16xy2 - 24y2z + 40y2
8y2
8y2
8y2
8y2(2x – 3z + 5)
Factor each monomial 1. Put parentheses around both
sets of monomials.
completely:
2. Find the GCF of each set of
( 2xy + 7x)(- 2y - 7)
binomials.
x
x -1 -1
3. Divide each term by the
x (2y + 7) - 1(2y + 7) GCF.
4. Take the two GCF’s and put
(x -1) (2y + 7)
them in parentheses together
5. Bring down what’s in the
other set of parentheses. These
parentheses should always look
just alike!
Find the roots: (x – 2) (4x – 1) = 0
or
Find the zeros
x – 2 = 0 or 4x – 1 = 0 1. The zero product
property
says
that
either
x=2
4x = 1
x – 2 = 0 or 4x – 1 = 0.
x = ¼ 2. Solve each equation for x.
3. The roots are what x =‘s.
Find the roots: 4y = 12y2
or
Find the zeros.
1. Set the equation = to zero.
- 12y2 + 4y = 0
4y
4y
2. Factor the GCF.
4y (- 3y + 1) = 0
3. Divide by the GCF.
4y = 0 Or -3y + 1 = 0 4. The zero product
property says that either
y=0
-3y = -1
4y = 0 or -3y + 1 = 0.
y = 1/3 5. Solve each equation for y.
6. The roots are what y =‘s.