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Quadratic Equations and Factoring Practice

Practice solving quadratic equations using factoring methods such as FOIL and the quadratic formula. Examples include multiplication of binomials, factoring quadratics, and using the quadratic formula for solutions.

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Quadratic Equations and Factoring Practice

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  1. Chapter 7 Section 7.6 Exercise #7

  2. Use the FOIL method to multiply the two binomials.

  3. Outer Inner First Last (2x  7)(7x  9)

  4. First Outer Inner Last 2x 7x + 2x  9 + 7 7x + 7 9

  5. 14x2  18x  49x + 63

  6. 14x2  67x + 63

  7. Chapter 7 Section 7.6 Exercise #11

  8. Solve the quadratic equation by factoring.

  9. x2 + 5x + 6 = 0 6 2 3 2 + 3 = 5 1 6 1 + 6 ≠ 5 or

  10. x2 + 5x + 6 = 0 (x + 3)(x + 2) = 0

  11. x2 + 5x + 6 = 0 If (x + 3) (x + 2) = 0 (x + 3) = 0 or (x + 2) = 0 then

  12. x2 + 5x + 6 = 0 (x + 3) = 0

  13. x2 + 5x + 6 = 0 x + 3  3 = 0  3

  14. x2 + 5x + 6 = 0 x = 3 or (x + 2) = 0

  15. x2 + 5x + 6 = 0 x = 3 or x + 2  2 = 0  2

  16. x2 + 5x + 6 = 0 x = 3 or x= 2

  17. x2 + 5x + 6 = 0 The solution set is{2,3}.

  18. check: (2)2 + 5(2) + 6

  19. check: 4  10 + 6

  20. check: 0 

  21. check: (3)2 + 5(3) + 6

  22. check: 9  15 + 6

  23. check: 0 

  24. Chapter 7 Section 7.6 Exercise #29

  25. Solve the quadratic equation by factoring.

  26. 12  x = 6x2 12  12  x + x = 6x2  12 + x

  27. 12  x = 6x2 0 = 6x2  12 + x

  28. 12  x = 6x2 0 = 6x2 + x  12

  29. 12  x = 6x2 If (3x  4)(2x + 3) = 0 then 3x  4 = 0 or 2x + 3 = 0

  30. 12  x = 6x2 (3x  4) = 0

  31. 12  x = 6x2 3x  4 + 4 = 0 + 4

  32. 12  x = 6x2 3 3 3x = 4

  33. 12  x = 6x2 4 1 x = 3

  34. 12  x = 6x2 4 x = 3 or (2x + 3) = 0

  35. 12  x = 6x2 4 x = 3 or 2x + 3  3 = 0  3

  36. 12  x = 6x2 4 x = 3 or 2x = 3 2 2

  37. 12  x = 6x2 4 x = 3 or 1 x = 3 2

  38. 12  x = 6x2 4 x = 3 or x = 3 2

  39. 12  x = 6x2 4 3 The solution set is{ , }. 3 2

  40. 12  = 6 4 4 3 3 check:

  41. check: 2 16  = 9 4 6 3 36 3 1 3

  42. check: = 32 32 3 3 

  43. 12  = 6 3 3 2 2 check:

  44. check: 3 + = 6 2 24 2 3 9 2 4

  45. check: 27 27 = 2 2 

  46. Chapter 7 Section 7.6 Exercise #37

  47. Solve the quadratic equation by using the quadratic formula.

  48. x2  8x  9 = 0 +

  49. x2  8x  9 = 0 +

  50. x2  8x  9 = 0 +

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