7 5 Factoring ax 2 bx c when

7. 5 Factoring ax 2 + bx + c when a=1 NOTES

Factor. 1. x 2 + 10 x +16 ac 16 2 a 1 8 a 1 a= 1 b= 10 c= 16 ___ 10 b (1 x+2)(1 x+8) On the left and right side, we need to find factors of ac that will have a sum = b. (x+2)(x+8) Use the FOIL method to check your answer. Use your yellow sheet to make a list Product 16 1 and 16 2 and 8 4 and 4 Sum=10

Factor. x 2 - 8 x + 12 2. a= 1 b= - 8 c= 12 ac 12 -2 a 1 ___ a 13 b (1 x - 2)(1 x - 6) -6 1 On the left and right side, we need to find factors of ac that will have a sum = b. (x - 2)(x - 6) Use the FOIL method to check your answer. Use your yellow sheet to make a list Product 12 1 and 12 2 and 6 3 and 4 Sum= - 8

Factor. x 2 + 4 x - 21 3. a= 1 b= 4 c= - 21 ac - 21 -3 a 1 7 1 ___ a 4 b Try Monitoring Progress 1 -3: Factor. MP 1: x 2 + 7 x + 6 (x + 1)(x + 6) MP 2: x 2 - 12 x + 35 (x - 5)(x - 7) On the left and right side, we need to find factors of ac that will have a sum = b. Use your (x - 3)(x + 7) yellow sheet Use the FOIL method to to make a list (1 x - 3)(1 x + 7) check your answer. MP 3: x 2 - 14 x + 24 (x - 2)(x - 12) Product - 21 1 and 21 3 and 7 Sum= 4

4. ac 27 -3 a 1 ___ a - 12 b (1 x - 3)(1 x - 9) =0 Factor and then solve for x. Move - 27 x 2 - 12 x = - 27 by adding x 2 - 12 x +27 = 0 a= 1 b= - 12 c= 27 -9 1 On the left and right side, we need to find factors of ac that will have a sum = b. (x - 3)(x - 9) =0 x – 3 = 0 x - 9 =0 x = 3 and x = 9 Try Monitoring Progress 4: Factor and then solve for x. MP 4: x 2 + 2 x = 15 x 2+2 x-15=0 (x - 3)(x + 5)= 0 x– 3=0 x+5=0 x=3 x=-5