1. Objective The student will be able to: use grouping to factor polynomials with four terms. SOL: A.2c Designed by Skip Tyler, Varina High School

2. 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

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 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)

6. 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 )