Transcript Factoring by Grouping

Objective
The student will be able to:
use grouping to factor
polynomials with four terms.
SOL: A.2c
Designed by Skip Tyler, Varina High School
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)