1. 10-2 Factoring Using the Distributive Property
Objectives
1. factor polynomials using the Distributive
Property.
2. solve quadratic equations of the form
ax2 + bx = 0.
Designed by Skip Tyler, Varina High School

2. Review: What is the GCF of 25a2 and 15a?
Let’s go one step further…
1) FACTOR 25a2 + 15a.
Find the GCF and divide each term
25a2 + 15a = 5a( ___ + ___ )
Check your answer by distributing. 5a 3

3. 2) Factor 18x2 - 12x3. Find the GCF 6x2 Divide each term by the GCF
18x2 - 12x3 = 6x2( ___ - ___ )
Check your answer by distributing. 3 2x

4. 3) Factor 28a2b + 56abc2. GCF = 28ab Divide each term by the GCF
28a2b + 56abc2 = 28ab ( ___ + ___ )
Check your answer by distributing.
28ab(a + 2c2) a
2c2

5. Factor 20x2 - 24xy
x(20 – 24y)
2x(10x – 12y)
4(5x2 – 6xy)
4x(5x – 6y)

6. 5) Factor 28a2 + 21b - 35b2c2 GCF = 7 Divide each term by the GCF
Check your answer by distributing.
7(4a2 + 3b – 5b2c2)
4a2 3b
5b2c2

7. Factor 16xy2 - 24y2z + 40y2 2y2(8x – 12z + 20) 4y2(4x – 6z + 10)
8xy2z(2 – 3 + 5)

8. Video—Factoring Using the GCF

9. What happens if your polynomial has 4 terms?

10. 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

11. 1. Factor 12ac + 21ad + 8bc + 14bd Do you have a GCF for all 4 terms?
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) No

12. 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)

13. 3. Factor 2x2 - 3xz - 2xy + 3yz Check for a GCF: None
Factor by grouping.
2x2 - 3xz - 2xy + 3yz
Find the GCF of each group.
x(2x - 3x) - y(2x - 3z)
Pay close attention to the signs in the second set of parentheses.
The parentheses are the same!
(x - y)(2x - 3z)

14. 4. Factor 16k3 - 4k2p2 - 28kp + 7p3 Check for a GCF: None
Factor by grouping.
16k3 - 4k2p kp + 7p3
Find the GCF of each group.
4k2(4k - p2) - 7p(4k - p2)
The signs are opposite in the parentheses!
(4k2 - 7p)(4k - p2)