1. X-box Factoring Quadratics February 5, 2016

2. Factor the x-box way Middle b= p + q Sum Product ac p q First and Last Coefficients y = ax 2 + bx + c Last term 1st Term Factor q Factor p x q x p

3. Factor the x-box way Example: Factor 3x 2 -13x -10 -13 (3)(-10)= -30 -15 2 -10 -15x 2x 3x 2 x-5 3x +2 3x 2 -13x -10 = (x-5)(3x+2)

4. Factor the x-box way Example: Factor 2x 2 + 11x + 5 (2)(5) = 10 5 10x x 2x 2 x 2x 1 2x 2 + 11x + 5 = (2x + 1)(x +5) 1 11 5

5. Factor the x-box way Example: Factor 5w 2 – 9w -2 (5)(-2) = -10 -2 -10x w 5w 2 w 5w 1 5w 2 – 9w -2 = (5w+1)(w-2) 1 -9 -2

6. Examples Factor using the x-box method. 1. x 2 + 4x – 12 a) b) x -12 4 6 -2 x 2 6x -2x -12 x -2 +6 Solution: x 2 + 4x – 12 = (x + 6)(x - 2)

7. Examples continued 2x 2 + 19 -10 -20 20 -1 19 x 2 20x -1x 10 2x2x Solution: 2x 2 + 19 -10 = (2x-1)(x+10) X 10

8. Think-Pair-Share 1.Based on the problems we ’ ve done, list the steps in the diamond/box factoring method so that you could teach someone else can do a problem. 2. Trade papers with your partner and use their steps to factor the following problem: 3b 2 + 26b +35

9. Trying out the Steps 3.If you cannot complete the problem using only the steps written, put an arrow on the step where you stopped. Give your partner ’ s paper back to him. 4.Modify the steps you wrote to correct any incomplete or incorrect steps. Finish the problem based on your new steps and give the steps back to your partner. 5.Try using the steps again to factor: 3x 2 - 17x -6.

10. Examples 2x 2 - 5x - 7 2x 2 -7x 2x -7 x 2x-7 +1 Solution: 2x 2 - 5x – 7 = (2x - 7)(x + 1 )

11. Examples 15x 2 + 7x - 2 a) b) -30 7 15x 2 10x -3x -2 5x 3x+2 Solution: 15x 2 + 7x – 2 = (3x + 2)(5x - 1 ) 10 -3

12. Independent Practice Show all work.