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8.3 – Factoring Trinomials: x 2 + b x + c

8.3 – Factoring Trinomials: x 2 + b x + c. Recall: Simplify ( x + 2)( x + 3). Recall: Simplify ( x + 2)( x + 3). ( x · x ). Recall: Simplify ( x + 2)( x + 3 ). ( x · x ) + ( x · 3). Recall: Simplify ( x + 2 )( x + 3). ( x · x ) + ( x · 3) + (2 · x ).

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8.3 – Factoring Trinomials: x 2 + b x + c

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  1. 8.3 – Factoring Trinomials: x2 + bx + c

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

  3. Recall: Simplify (x + 2)(x + 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) x2 + 3x + 2x + 6

  8. Recall: Simplify (x + 2)(x + 3). (x · x) + (x · 3) + (2 · x) + (2 · 3) x2 + 3x + 2x + 6 x2 + (3 + 2)x + 6

  9. Recall: Simplify (x + 2)(x + 3). (x · x) + (x · 3) + (2 · x) + (2 · 3) x2 + 3x + 2x + 6 x2 + (3 + 2)x + 6 x2 + 5x + 6

  10. Recall: Simplify (x + 2)(x + 3). (x · x) + (x · 3) + (2 · x) + (2 · 3) x2 + 3x + 2x + 6 x2 + (3 + 2)x + 6 x2 + 5x + 6 Ex. 1 Factor x2 + 5x + 6.

  11. Recall: Simplify (x + 2)(x + 3). (x · x) + (x · 3) + (2 · x) + (2 · 3) x2 + 3x + 2x + 6 x2 + (3 + 2)x + 6 x2 + 5x + 6 Ex. 1 Factor x2 + 5x + 6. (x )(x )

  12. Recall: Simplify (x + 2)(x + 3). (x · x) + (x · 3) + (2 · x) + (2 · 3) x2 + 3x + 2x + 6 x2 + (3 + 2)x + 6 x2 + 5x + 6 Ex. 1 Factor x2 + 5x + 6. (x )(x ) ax2 + bx + c = (x + m)(x + n) such that m + n = b and mn = c

  13. Ex. 2 Factor x2 + 6x + 8.

  14. Ex. 2 Factor x2 + 6x + 8. x2 + 6x + 8 = (x )(x )

  15. Ex. 2 Factor x2 + 6x + 8. x2 + 6x + 8 = (x )(x ) = (x + 2)(x + 4)

  16. Ex. 2 Factor x2 + 6x + 8. x2 + 6x + 8 = (x )(x ) = (x + 2)(x + 4) Ex. 3 Factor x2 – 10x + 16.

  17. Ex. 2 Factor x2 + 6x + 8. x2 + 6x + 8 = (x )(x ) = (x + 2)(x + 4) Ex. 3 Factor x2 – 10x + 16. x2 – 10x + 16 = (x )(x )

  18. Ex. 2 Factor x2 + 6x + 8. x2 + 6x + 8 = (x )(x ) = (x + 2)(x + 4) Ex. 3 Factor x2 – 10x + 16. x2 – 10x + 16 = (x )(x ) = (x – 2)(x – 8)

  19. Ex. 2 Factor x2 + 6x + 8. x2 + 6x + 8 = (x )(x ) = (x + 2)(x + 4) Ex. 3 Factor x2 – 10x + 16. x2 – 10x + 16 = (x )(x ) = (x – 2)(x – 8) Ex. 4 Factor x2 + x – 12.

  20. Ex. 2 Factor x2 + 6x + 8. x2 + 6x + 8 = (x )(x ) = (x + 2)(x + 4) Ex. 3 Factor x2 – 10x + 16. x2 – 10x + 16 = (x )(x ) = (x – 2)(x – 8) Ex. 4 Factor x2 + x – 12. x2 + x – 12 = (x )(x )

  21. Ex. 2 Factor x2 + 6x + 8. x2 + 6x + 8 = (x )(x ) = (x + 2)(x + 4) Ex. 3 Factor x2 – 10x + 16. x2 – 10x + 16 = (x )(x ) = (x – 2)(x – 8) Ex. 4 Factor x2 + x – 12. x2 + x – 12 = (x )(x ) = (x + 4)(x – 3)

  22. Ex. 5 Factor x2 – 7x – 18.

  23. Ex. 5 Factor x2 – 7x – 18. x2 – 7x – 18 = (x )(x )

  24. Ex. 5 Factor x2 – 7x – 18. x2 – 7x – 18 = (x )(x ) = (x + 2)(x – 9)

  25. Ex. 5 Factor x2 – 7x – 18. x2 – 7x – 18 = (x )(x ) = (x + 2)(x – 9) Ex. 6 Solve x2 + 5x = 6.

  26. Ex. 5 Factor x2 – 7x – 18. x2 – 7x – 18 = (x )(x ) = (x + 2)(x – 9) Ex. 6 Solve x2 + 5x = 6. x2 + 5x = 6 -6 -6

  27. Ex. 5 Factor x2 – 7x – 18. x2 – 7x – 18 = (x )(x ) = (x + 2)(x – 9) Ex. 6 Solve x2 + 5x = 6. x2 + 5x = 6 -6 -6 x2 + 5x – 6 = 0

  28. Ex. 5 Factor x2 – 7x – 18. x2 – 7x – 18 = (x )(x ) = (x + 2)(x – 9) Ex. 6 Solve x2 + 5x = 6. x2 + 5x = 6 -6 -6 x2 + 5x – 6 = 0 (x )(x ) = 0

  29. Ex. 5 Factor x2 – 7x – 18. x2 – 7x – 18 = (x )(x ) = (x + 2)(x – 9) Ex. 6 Solve x2 + 5x = 6. x2 + 5x = 6 -6 -6 x2 + 5x – 6 = 0 (x )(x ) = 0 (x – 1)(x + 6) = 0

  30. Ex. 5 Factor x2 – 7x – 18. x2 – 7x – 18 = (x )(x ) = (x + 2)(x – 9) Ex. 6 Solve x2 + 5x = 6. x2 + 5x = 6 -6 -6 x2 + 5x – 6 = 0 (x )(x ) = 0 (x – 1)(x + 6) = 0 x – 1 = 0 x + 6 = 0

  31. Ex. 5 Factor x2 – 7x – 18. x2 – 7x – 18 = (x )(x ) = (x + 2)(x – 9) Ex. 6 Solve x2 + 5x = 6. x2 + 5x = 6 -6 -6 x2 + 5x – 6 = 0 (x )(x ) = 0 (x – 1)(x + 6) = 0 x – 1 = 0 x + 6 = 0 x = 1 x= -6

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