1. 8.3 – Factoring Trinomials: x 2 + bx + c

2. Recall: Simplify (x + 2)(x + 3).

3. (x · x)

4. Recall: Simplify (x + 2)(x + 3). (x · x) + (x · 3)

5. Recall: Simplify (x + 2)(x + 3). (x · x) + (x · 3) + (2 · x)

6. Recall: Simplify (x + 2)(x + 3). (x · x) + (x · 3) + (2 · x) + (2 · 3)

7. Recall: Simplify (x + 2)(x + 3). (x · x) + (x · 3) + (2 · x) + (2 · 3) x 2 + 3x + 2x + 6

8. Recall: Simplify (x + 2)(x + 3). (x · x) + (x · 3) + (2 · x) + (2 · 3) x 2 + 3x + 2x + 6 x 2 + (3 + 2)x + 6

9. Recall: Simplify (x + 2)(x + 3). (x · x) + (x · 3) + (2 · x) + (2 · 3) x 2 + 3x + 2x + 6 x 2 + (3 + 2)x + 6 x 2 + 5x + 6

10. Recall: Simplify (x + 2)(x + 3). (x · x) + (x · 3) + (2 · x) + (2 · 3) x 2 + 3x + 2x + 6 x 2 + (3 + 2)x + 6 x 2 + 5x + 6 Ex. 1 Factor x 2 + 5x + 6.

11. Recall: Simplify (x + 2)(x + 3). (x · x) + (x · 3) + (2 · x) + (2 · 3) x 2 + 3x + 2x + 6 x 2 + (3 + 2)x + 6 x 2 + 5x + 6 Ex. 1 Factor x 2 + 5x + 6. (x )(x)

12. Recall: Simplify (x + 2)(x + 3). (x · x) + (x · 3) + (2 · x) + (2 · 3) x 2 + 3x + 2x + 6 x 2 + (3 + 2)x + 6 x 2 + 5x + 6 Ex. 1 Factor x 2 + 5x + 6. (x )(x) ax 2 + bx + c = (x + m)(x + n) such that m + n = b and mn = c

13. Ex. 2 Factor x 2 + 6x + 8.

14. x 2 + 6x + 8 = (x )(x)

15. Ex. 2 Factor x 2 + 6x + 8. x 2 + 6x + 8 = (x )(x) = (x + 2)(x + 4)

16. Ex. 2 Factor x 2 + 6x + 8. x 2 + 6x + 8 = (x )(x) = (x + 2)(x + 4) Ex. 3 Factor x 2 – 10x + 16.

17. Ex. 2 Factor x 2 + 6x + 8. x 2 + 6x + 8 = (x )(x) = (x + 2)(x + 4) Ex. 3 Factor x 2 – 10x + 16. x 2 – 10x + 16 = (x )(x)

18. Ex. 2 Factor x 2 + 6x + 8. x 2 + 6x + 8 = (x )(x) = (x + 2)(x + 4) Ex. 3 Factor x 2 – 10x + 16. x 2 – 10x + 16 = (x )(x) = (x – 2)(x – 8)

19. Ex. 2 Factor x 2 + 6x + 8. x 2 + 6x + 8 = (x )(x) = (x + 2)(x + 4) Ex. 3 Factor x 2 – 10x + 16. x 2 – 10x + 16 = (x )(x) = (x – 2)(x – 8) Ex. 4 Factor x 2 + x – 12.

20. Ex. 2 Factor x 2 + 6x + 8. x 2 + 6x + 8 = (x )(x) = (x + 2)(x + 4) Ex. 3 Factor x 2 – 10x + 16. x 2 – 10x + 16 = (x )(x) = (x – 2)(x – 8) Ex. 4 Factor x 2 + x – 12. x 2 + x – 12 = (x )(x)

21. Ex. 2 Factor x 2 + 6x + 8. x 2 + 6x + 8 = (x )(x) = (x + 2)(x + 4) Ex. 3 Factor x 2 – 10x + 16. x 2 – 10x + 16 = (x )(x) = (x – 2)(x – 8) Ex. 4 Factor x 2 + x – 12. x 2 + x – 12 = (x )(x) = (x + 4)(x – 3)

22. Ex. 5 Factor x 2 – 7x – 18.

23. x 2 – 7x – 18 = (x )(x)

24. Ex. 5 Factor x 2 – 7x – 18. x 2 – 7x – 18 = (x )(x) = (x + 2)(x – 9)

25. Ex. 5 Factor x 2 – 7x – 18. x 2 – 7x – 18 = (x )(x) = (x + 2)(x – 9) Ex. 6 Solve x 2 + 5x = 6.

26. Ex. 5 Factor x 2 – 7x – 18. x 2 – 7x – 18 = (x )(x) = (x + 2)(x – 9) Ex. 6 Solve x 2 + 5x = 6. x 2 + 5x = 6 -6 -6

27. Ex. 5 Factor x 2 – 7x – 18. x 2 – 7x – 18 = (x )(x) = (x + 2)(x – 9) Ex. 6 Solve x 2 + 5x = 6. x 2 + 5x = 6 -6 -6 x 2 + 5x – 6 = 0

28. Ex. 5 Factor x 2 – 7x – 18. x 2 – 7x – 18 = (x )(x) = (x + 2)(x – 9) Ex. 6 Solve x 2 + 5x = 6. x 2 + 5x = 6 -6 -6 x 2 + 5x – 6 = 0 (x )(x) = 0

29. Ex. 5 Factor x 2 – 7x – 18. x 2 – 7x – 18 = (x )(x) = (x + 2)(x – 9) Ex. 6 Solve x 2 + 5x = 6. x 2 + 5x = 6 -6 -6 x 2 + 5x – 6 = 0 (x )(x) = 0 (x – 1)(x + 6) = 0

30. Ex. 5 Factor x 2 – 7x – 18. x 2 – 7x – 18 = (x )(x) = (x + 2)(x – 9) Ex. 6 Solve x 2 + 5x = 6. x 2 + 5x = 6 -6 -6 x 2 + 5x – 6 = 0 (x )(x) = 0 (x – 1)(x + 6) = 0 x – 1 = 0x + 6 = 0

31. Ex. 5 Factor x 2 – 7x – 18. x 2 – 7x – 18 = (x )(x) = (x + 2)(x – 9) Ex. 6 Solve x 2 + 5x = 6. x 2 + 5x = 6 -6 -6 x 2 + 5x – 6 = 0 (x )(x) = 0 (x – 1)(x + 6) = 0 x – 1 = 0x + 6 = 0 x = 1 x= -6