1. Bottoms Up Factoring

2. Start with the X-box 3-9 Product Sum -6 -27

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

4. Examples x 2 - 9x + 20 -9 20 Solution: x 2 - 9x + 20 = (x - 4)(x - 5 ) -4 -5 (x - 4)(x - 5)

5. Examples 2x 2 + 7x + 3 6 7 6 1 (x + 6) ( x + 1) 2 x 2 + 7x + 3 = (x + 3) ( 2 x + 1) (x + 6) ( x + 1) 2 2

6. Examples Factor 3x 2 -13x -10 -13 (3)(-10)= -30 -15 2 3x 2 -13x -10 = (x-5)(3x+2) (X – 15) (x + 2) 3 3 (X –5) (3x + 2)

7. Stepping Up- Your Turn factor: 3x 2 + 11x – 20

8. Stepping Up-Your Turn factor: 3x 2 + 11x – 20. 11 -60 15 -4 3x 2 + 11x – 20 = (x + 5) (3x - 4) (x +15) (x – 4) 3 3 (x +5) (3x – 4)

9. Examples continued 2x 2 - 5x - 7 -5 -14 Solution: 2x 2 - 5x – 7 = (2x - 7)(x + 1) -7 2 (x - 7)(x + 2) 2 (2x - 7)(x + 1)

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

11. Trying out the Steps Factor: 4x 2 +4x -3

12. So: 4x 2 +4x -3 = (2x + 3) (2x -1) 4x 2 +4x -3 4 -12 6 -2 (x +6) (x – 2) 4 (x +3) (x – 1) 2 Stepping Up- Your Turn