Download Factoring GCF

Objectives
The student will be able to:
MFCR Ch. 4-4 GCF and Factoring
by Grouping 1-7-14
1. find the greatest common factor (GCF) for
a set of monomials.
The Greatest Common Factor
(GCF) of 2 or more numbers is
the largest number that can divide
into all of the numbers.
4) Find the GCF of 42 and 60.
4) Find the GCF of 42 and 60.
42 =
60 =
2 • 3 • 7
2•2•3•5
What prime factors do the numbers
have in common?
Multiply those numbers.
The GCF is 2 • 3 = 6
6 is the largest number that can go
into 42 and 60!
5) Find the GCF of 40a2b and 48ab4.
40a2b = 2 • 2 • 2 • 5 •
a•a•b
48ab4 = 2 • 2 • 2 • 2 • 3 • a • b • b • b • b
What do they have in common?
Multiply the factors together.
GCF = 8ab
What is the GCF of 48 and 64?
1.
2.
3.
4.
2
4
8
16
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 18x2 - 12x3.
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.
3) Factor
2
28a b
+
2
56abc .
GCF = 28ab
Divide each term by the GCF
28a2b + 56abc2 = 28ab ( ___
a + ___
2c2 )
28a 2b
28ab
56abc 2
28ab
Check your answer by distributing.
28ab(a + 2c2)
Factor
1.
2.
3.
4.
x(20 – 24y)
2x(10x – 12y)
4(5x2 – 6xy)
4x(5x – 6y)
2
20x
- 24xy
5) Factor 28a2 + 21b - 35b2c2
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)
Factor
1.
2.
3.
4.
2
16xy
2y2(8x – 12z + 20)
4y2(4x – 6z + 10)
8y2(2x - 3z + 5)
8xy2z(2 – 3 + 5)
-
2
24y z
+
2
40y
Objective
The student will be able to:
use grouping to factor
polynomials with four terms.
Factoring Chart
This chart will help you to determine
which method of factoring to use.
Type
Number of Terms
1. GCF
2. Grouping
2 or more
4
1. Factor 12ac + 21ad + 8bc + 14bd
Do you have a GCF for all 4 terms? No
Group the first 2 terms and the last 2 terms.
(12ac + 21ad) + (8bc + 14bd)
Find the GCF of each group.
3a (4c + 7d) + 2b(4c + 7d)
The parentheses are the same!
(3a + 2b)(4c + 7d)
2. Factor rx + 2ry + kx + 2ky
Check for a GCF: None
You have 4 terms - try factoring by grouping.
(rx + 2ry) + (kx + 2ky)
Find the GCF of each group.
r(x + 2y) + k(x + 2y)
The parentheses are the same!
(r + k)(x + 2y)
3. Factor
2
2x
- 3xz - 2xy + 3yz
Check for a GCF: None
Factor by grouping. Keep a + between the groups.
(2x2 - 3xz) + (- 2xy + 3yz)
Find the GCF of each group.
x(2x – 3z) + y(- 2x + 3z)
The signs are opposite in the parentheses!
Keep-change-change!
x(2x - 3x) - y(2x - 3z)
(x - y)(2x - 3z)
4. Factor
3
16k
-
2
2
4k p
- 28kp +
3
7p
Check for a GCF: None
Factor by grouping. Keep a + between the groups.
(16k3 - 4k2p2 ) + (-28kp + 7p3)
Find the GCF of each group.
4k2(4k - p2) + 7p(-4k + p2)
The signs are opposite in the parentheses!
Keep-change-change!
4k2(4k - p2) - 7p(4k - p2)
(4k2 - 7p)(4k - p2)