1. Objectives The student will be able to: MFCR Ch
Objectives The student will be able to: MFCR Ch. 4-4 GCF and Factoring by Grouping
1. find the greatest common factor (GCF) for a set of monomials.

2. 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.

3. 6 is the largest number that can go into 42 and 60!
4) Find the GCF of 42 and 60.
= 2 •  • 7
60 = 2 • 2 • 3 • 5
The GCF is 2 • 3 = 6
6 is the largest number that can go into 42 and 60!

4. 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

5. What is the GCF of 48 and 64? 2 4 8 16

6. Objectives The student will be able to:
Factor using the greatest common factor (GCF).

7. 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

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

9. 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

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

11. 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

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

13. Objective The student will be able to:
use grouping to factor polynomials with four terms.

14. 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

15. 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)

16. 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)

17. 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 – 3z) - y(2x - 3z)
(x - y)(2x - 3z)

18. 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)