1. I can use grouping to factor polynomials with four terms.

2. Factoring Chart This chart will help you to determine which method of factoring to use. Type Number of Terms
1. GCF or more
2. Grouping 4

3. 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)

4. 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)

5. 3. Factor 2x2 - 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)

6. 4. Factor 16k3 - 4k2p2 - 28kp + 7p3 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)

7. Zero Product Property If a • b = 0 then a=0, b=0,
or both a and b equal 0.

8. 1. Solve (x + 3)(x - 5) = 0
Using the Zero Product Property, you know that either x + 3 = 0 or x - 5 = 0
Solve each equation.
x = -3 or x = 5
{-3, 5}

9. 3t + 5 = 0 or t - 3 = 0 3t = -5 or t = 3 t = -5/3 or t = 3 {-5/3, 3}
3. Solve (3t + 5)(t - 3) = 0
3t + 5 = 0 or t - 3 = 0
3t = -5 or t = 3
t = -5/3 or t = 3
{-5/3, 3}

10. 4. Solve x2 - 11x = 0 GCF = x x(x - 11) = 0 x = 0 or x - 11 = 0
{0, 11}
Set = 0
Factor
Split/Solve
Check