Objectives The student will be able to MFCR
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.
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.
4) Find the GCF of 42 and 60. 42 = 60 = 2 • 3 • 7 2 • 3 • 5 The GCF is 2 • 3 = 6 6 is the largest number that can go into 42 and 60!
5) Find the GCF of 40 a 2 b and 48 ab 4. 40 a 2 b = 2 • 2 • 5 • a • b 48 ab 4 = 2 • 2 • 3 • a • b • b What do they have in common? Multiply the factors together. GCF = 8 ab
What is the GCF of 48 and 64? 1. 2. 3. 4. 2 4 8 16
Objectives The student will be able to: Factor using the greatest common factor (GCF).
Review: What is the GCF of 25 a 2 and 15 a? 5 a Let’s go one step further… 1) FACTOR 25 a 2 + 15 a. Find the GCF and divide each term 25 a 2 + 15 a = 5 a( ___ + ___ ) 5 a 3 Check your answer by distributing.
2) Factor 18 x 2 - 12 x 3. Find the GCF 6 x 2 Divide each term by the GCF 18 x 2 - 12 x 3 = 6 x 2( ___ - ___ ) 3 2 x Check your answer by distributing.
2 2 3) Factor 28 a b + 56 abc. GCF = 28 ab Divide each term by the GCF 2 2 2 a 2 c 28 a b + 56 abc = 28 ab ( ___ + ___ ) Check your answer by distributing. 28 ab(a + 2 c 2)
2 Factor 20 x - 24 xy 1. 2. 3. 4. x(20 – 24 y) 2 x(10 x – 12 y) 4(5 x 2 – 6 xy) 4 x(5 x – 6 y)
5) Factor 28 a 2 + 21 b - 35 b 2 c 2 GCF = 7 Divide each term by the GCF 4 a 2 3 b 5 b 2 c 2 28 a 2 + 21 b - 35 b 2 c 2 = 7 ( ___ + ___ - ____ ) Check your answer by distributing. 7(4 a 2 + 3 b – 5 b 2 c 2)
2 2 2 Factor 16 xy - 24 y z + 40 y 1. 2. 3. 4. 2 y 2(8 x – 12 z + 20) 4 y 2(4 x – 6 z + 10) 8 y 2(2 x - 3 z + 5) 8 xy 2 z(2 – 3 + 5)
Objective The student will be able to: use grouping to factor polynomials with four terms.
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 12 ac + 21 ad + 8 bc + 14 bd Do you have a GCF for all 4 terms? No Group the first 2 terms and the last 2 terms. (12 ac + 21 ad) + (8 bc + 14 bd) Find the GCF of each group. 3 a (4 c + 7 d) + 2 b(4 c + 7 d) The parentheses are the same! (3 a + 2 b)(4 c + 7 d)
2. Factor rx + 2 ry + kx + 2 ky Check for a GCF: None You have 4 terms - try factoring by grouping. (rx + 2 ry) + (kx + 2 ky) Find the GCF of each group. r(x + 2 y) + k(x + 2 y) The parentheses are the same! (r + k)(x + 2 y)
2 3. Factor 2 x - 3 xz - 2 xy + 3 yz Check for a GCF: None Factor by grouping. Keep a + between the groups. (2 x 2 - 3 xz) + (- 2 xy + 3 yz) Find the GCF of each group. x(2 x – 3 z) + y(- 2 x + 3 z) The signs are opposite in the parentheses! Keep-change! x(2 x – 3 z) - y(2 x - 3 z) (x - y)(2 x - 3 z)
3 2 2 3 4. Factor 16 k - 4 k p - 28 kp + 7 p Check for a GCF: None Factor by grouping. Keep a + between the groups. (16 k 3 - 4 k 2 p 2 ) + (-28 kp + 7 p 3) Find the GCF of each group. 4 k 2(4 k - p 2) + 7 p(-4 k + p 2) The signs are opposite in the parentheses! Keep-change! 4 k 2(4 k - p 2) - 7 p(4 k - p 2) (4 k 2 - 7 p)(4 k - p 2)
- Slides: 18