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8.4 – Factoring Trinomials: a x 2 + b x + c

8.4 – Factoring Trinomials: a x 2 + b x + c. Recall : Factor x 2 + 5 x + 6. Recall : Factor x 2 + 5 x + 6 ( x )( x ). Recall : Factor x 2 + 5 x + 6 ( x )( x ) x 2 + 2 x + 3 x + 6 *2 factors of 6 that add up to 5!.

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8.4 – Factoring Trinomials: a x 2 + b x + c

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  1. 8.4 – Factoring Trinomials: ax2 + bx + c

  2. Recall: Factor x2 + 5x + 6

  3. Recall: Factor x2 + 5x + 6 (x )(x )

  4. Recall: Factor x2 + 5x + 6 (x )(x ) x2 + 2x + 3x + 6 *2 factors of 6 that add up to 5!

  5. Recall: Factor x2 + 5x + 6 (x )(x ) x2 + 2x + 3x + 6 *2 factors of 6 that add up to 5! Factor 2x2 + 7x + 6.

  6. Recall: Factor x2 + 5x + 6 (x )(x ) x2 + 2x + 3x + 6 *2 factors of 6 that add up to 5! Factor 2x2 + 7x + 6. *2 factors of 12 that add up to 7!

  7. Recall: Factor x2 + 5x + 6 (x )(x ) x2 + 2x + 3x + 6 *2 factors of 6 that add up to 5! Factor 2x2 + 7x + 6. *2 factors of 12 that add up to 7! 2x2 + x + x + 6

  8. Recall: Factor x2 + 5x + 6 (x )(x ) x2 + 2x + 3x + 6 *2 factors of 6 that add up to 5! Factor 2x2 + 7x + 6. *2 factors of 12 that add up to 7! 2x2 + x + x + 6 2x2 + 4x + 3x + 6

  9. Recall: Factor x2 + 5x + 6 (x )(x ) x2 + 2x + 3x + 6 *2 factors of 6 that add up to 5! Factor 2x2 + 7x + 6. *2 factors of 12 that add up to 7! 2x2 + x + x + 6 2x2 + 4x + 3x + 6 2x(x + 2) + 3(x + 2)

  10. Recall: Factor x2 + 5x + 6 (x )(x ) x2 + 2x + 3x + 6 *2 factors of 6 that add up to 5! Factor 2x2 + 7x + 6. *2 factors of 12 that add up to 7! 2x2 + x + x + 6 2x2 + 4x + 3x + 6 2x(x + 2) + 3(x + 2) (x + 2)(2x + 3)

  11. Ex. 1 Factor 4x2 + 14x – 8.

  12. Ex. 1 Factor 4x2 + 14x – 8. 2(2x2 + 7x – 4)

  13. Ex. 1 Factor 4x2 + 14x – 8. 2(2x2 + 7x– 4) 2[2x2 + x + x – 4]

  14. Ex. 1 Factor 4x2 + 14x – 8. 2(2x2 + 7x– 4) 2[2x2 + x + x – 4] 2[2x2– x+8x – 4]

  15. Ex. 1 Factor 4x2 + 14x – 8. 2(2x2 + 7x – 4) 2[2x2 + x + x – 4] 2[2x2 – x + 8x – 4] 2[x(2x – 1) + 4(2x – 1)]

  16. Ex. 1 Factor 4x2 + 14x – 8. 2(2x2 + 7x – 4) 2[2x2 + x + x – 4] 2[2x2 – x + 8x – 4] 2[x(2x – 1) + 4(2x – 1)] 2[(2x – 1)(x + 4)]

  17. Ex. 1 Factor 4x2 + 14x – 8. 2(2x2 + 7x – 4) 2[2x2 + x + x – 4] 2[2x2 – x + 8x – 4] 2[x(2x – 1) + 4(2x – 1)] 2[(2x – 1)(x + 4)] Ex. 2 Factor 2x2 – 5x + 2.

  18. Ex. 1 Factor 4x2 + 14x – 8. 2(2x2 + 7x – 4) 2[2x2 + x + x – 4] 2[2x2 – x + 8x – 4] 2[x(2x – 1) + 4(2x – 1)] 2[(2x – 1)(x + 4)] Ex. 2 Factor 2x2 – 5x + 2. 2x2 + x + x + 2

  19. Ex. 1 Factor 4x2 + 14x – 8. 2(2x2 + 7x – 4) 2[2x2 + x + x – 4] 2[2x2 – x + 8x – 4] 2[x(2x – 1) + 4(2x – 1)] 2[(2x – 1)(x + 4)] Ex. 2 Factor 2x2 – 5x + 2. 2x2 + x + x + 2 2x2 – x – 4x + 2

  20. Ex. 1 Factor 4x2 + 14x – 8. 2(2x2 + 7x – 4) 2[2x2 + x + x – 4] 2[2x2 – x + 8x – 4] 2[x(2x – 1) + 4(2x – 1)] 2[(2x – 1)(x + 4)] Ex. 2 Factor 2x2 – 5x + 2. 2x2 + x + x + 2 2x2 – x – 4x + 2 x(2x – 1) – 2(2x – 1)

  21. Ex. 1 Factor 4x2 + 14x – 8. 2(2x2 + 7x – 4) 2[2x2 + x + x – 4] 2[2x2 – x + 8x – 4] 2[x(2x – 1) + 2(2x – 1)] 2[(2x – 1)(x + 2)] Ex. 2 Factor 2x2 – 5x + 2. 2x2 + x + x + 2 2x2 – x – 4x + 2 x(2x – 1) – 2(2x – 1) (2x – 1)(x – 2)

  22. Ex. 3 Solve 8a2 – 9a – 5 = 4 – 3a. Check your solutions.

  23. Ex. 3 Solve 8a2 – 9a – 5 = 4 – 3a. Check your solutions. 8a2 – 9a – 5 = 4 – 3a

  24. Ex. 3 Solve 8a2 – 9a – 5 = 4 – 3a. Check your solutions. 8a2 – 9a – 5 = 4 – 3a +3a -4 -4 + 3a

  25. Ex. 3 Solve 8a2 – 9a – 5 = 4 – 3a. Check your solutions. 8a2 – 9a – 5 = 4 – 3a +3a -4 -4 + 3a 8a2 – 6a – 9 = 0

  26. Ex. 3 Solve 8a2 – 9a – 5 = 4 – 3a. Check your solutions. 8a2 – 9a – 5 = 4 – 3a +3a -4 -4 + 3a 8a2 – 6a– 9 = 0 8a2 + a + a – 9 = 0

  27. Ex. 3 Solve 8a2 – 9a – 5 = 4 – 3a. Check your solutions. 8a2 – 9a – 5 = 4 – 3a +3a -4 -4 + 3a 8a2 – 6a – 9 = 0 8a2 + a + a – 9 = 0 8a2 – 12a + 6a – 9 = 0

  28. Ex. 3 Solve 8a2 – 9a – 5 = 4 – 3a. Check your solutions. 8a2 – 9a – 5 = 4 – 3a +3a -4 -4 + 3a 8a2 – 6a – 9 = 0 8a2 + a + a – 9 = 0 8a2 – 12a + 6a – 9 = 0 4a(2a – 3)+ 3(2a – 3) = 0

  29. Ex. 3 Solve 8a2 – 9a – 5 = 4 – 3a. Check your solutions. 8a2 – 9a – 5 = 4 – 3a +3a -4 -4 + 3a 8a2 – 6a – 9 = 0 8a2 + a + a – 9 = 0 8a2 – 12a + 6a – 9 = 0 4a(2a – 3)+ 3(2a – 3) = 0 (2a – 3)(4a + 3) = 0

  30. Ex. 3 Solve 8a2 – 9a – 5 = 4 – 3a. Check your solutions. 8a2 – 9a – 5 = 4 – 3a +3a -4 -4 + 3a 8a2 – 6a – 9 = 0 8a2 + a + a – 9 = 0 8a2 – 12a + 6a – 9 = 0 4a(2a – 3)+ 3(2a – 3) = 0 (2a – 3)(4a + 3) = 0 2a – 3 = 0 4a + 3 = 0

  31. Ex. 3 Solve 8a2 – 9a – 5 = 4 – 3a. Check your solutions. 8a2 – 9a – 5 = 4 – 3a +3a -4 -4 + 3a 8a2 – 6a – 9 = 0 8a2 + a + a – 9 = 0 8a2 – 12a + 6a – 9 = 0 4a(2a – 3)+ 3(2a – 3) = 0 (2a – 3)(4a + 3) = 0 2a – 3 = 0 4a + 3 = 0 2a = 3 4a = -3

  32. Ex. 3 Solve 8a2 – 9a – 5 = 4 – 3a. Check your solutions. 8a2 – 9a – 5 = 4 – 3a +3a -4 -4 + 3a 8a2 – 6a – 9 = 0 8a2 + a + a – 9 = 0 8a2 – 12a + 6a – 9 = 0 4a(2a – 3)+ 3(2a – 3) = 0 (2a – 3)(4a + 3) = 0 2a – 3 = 0 4a + 3 = 0 2a = 3 4a = -3 a = 3/2 a = -3/4

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