1. 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.

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. 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! 42 =2 3 7 60=2 2 3 5

4. 5) Find the GCF of 40a 2 b and 48ab 4. 40a 2 b = 2 2 2 5 a a b 48ab 4 = 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? 1.2 2.4 3.8 4.16

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

7. Review: What is the GCF of 25a 2 and 15a? 5a Let’s go one step further… 1) FACTOR 25a 2 + 15a. Find the GCF and divide each term 25a 2 + 15a = 5a( ___ + ___ ) Check your answer by distributing. 5a3

8. 2) Factor 18x 2 - 12x 3. Find the GCF 6x 2 Divide each term by the GCF 18x 2 - 12x 3 = 6x 2 ( ___ - ___ ) Check your answer by distributing. 32x

9. 3) Factor 28a 2 b + 56abc 2. GCF = 28ab Divide each term by the GCF 28a 2 b + 56abc 2 = 28ab ( ___ + ___ ) Check your answer by distributing. 28ab(a + 2c 2 ) a2c 2

10. Factor 20x 2 - 24xy 1.x(20 – 24y) 2.2x(10x – 12y) 3.4(5x 2 – 6xy) 4.4x(5x – 6y)

11. 5) Factor 28a 2 + 21b - 35b 2 c 2 GCF = 7 Divide each term by the GCF 28a 2 + 21b - 35b 2 c 2 = 7 ( ___ + ___ - ____ ) Check your answer by distributing. 7(4a 2 + 3b – 5b 2 c 2 ) 4a 2 5b 2 c 2 3b

12. Factor 16xy 2 - 24y 2 z + 40y 2 1.2y 2 (8x – 12z + 20) 2.4y 2 (4x – 6z + 10) 3.8y 2 (2x - 3z + 5) 4.8xy 2 z(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. TypeNumber of Terms 1. GCF 2 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 2x 2 - 3xz - 2xy + 3yz Check for a GCF: None Factor by grouping. Keep a + between the groups. (2x 2 - 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)

18. 4. Factor 16k 3 - 4k 2 p 2 - 28kp + 7p 3 Check for a GCF: None Factor by grouping. Keep a + between the groups. (16k 3 - 4k 2 p 2 ) + (-28kp + 7p 3 ) Find the GCF of each group. 4k 2 (4k - p 2 ) + 7p(-4k + p 2 ) The signs are opposite in the parentheses! Keep-change-change! 4k 2 (4k - p 2 ) - 7p(4k - p 2 ) (4k 2 - 7p)(4k - p 2 )