1. 8.2B Factoring by Grouping Objectives The student will be able to: use grouping to factor polynomials with four terms use the zero product property to solve equations

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. Ex 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. Ex 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. Ex 3) 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 )

6. Zero Product Property If a b = 0 then a=0, b=0, or both a and b equal 0.

7. Ex 4) Solve (2a + 4)(a + 7) = 0 2a + 4 = 0 or a + 7 = 0 2a = – 4 or a = – 7 a = – 2 or a = – 7 {– 2, – 7}

8. 4 steps for solving a quadratic equation 1.Set the equation equal to 0. 2.Factor the equation. 3.Set each part equal to 0 and solve. 4.Check your answer on the calculator. Set = 0 Factor Split/Solve Check

9. Ex 5) Solve: x 2 – 11x = 0 GCF = x x(x – 11) = 0 x = 0 or x – 11 = 0 x = 0 or x = 11 {0, 11} Set = 0 Factor Split/Solve Check

10. Ex 6) Solve: – 24a +144 = – a 2 Put it in descending order. a 2 – 24a + 144 = 0 (a – 12) 2 = 0 a – 12 = 0 a = 12 {12} Set = 0 Factor Split/Solve Check

11. Ex 7) Solve: x 3 + 2x 2 = 15x x 3 + 2x 2 – 15x = 0 x(x 2 + 2x – 15) = 0 x(x + 5)(x – 3) = 0 x = 0 or x + 5 = 0 or x – 3 = 0 {0, – 5, 3} Set = 0 Factor Split/Solve Check

12. 8.2B HW PG. 479 #5 – 13 ODDS, 21 – 41 ODDS (16 PROBLEMS)