Extra Section
                   Synthetic Division



Fo r us e w it h li nea r fact ors
Warm-up
          Divide.
(3x + 2x − x + 3) ÷ (x − 3)
   3     2
Warm-up
                        Divide.
           (3x + 2x − x + 3) ÷ (x − 3)
                 3    2




x − 3 3x + 2x −...
Warm-up
                         Divide.
              (3x + 2x − x + 3) ÷ (x − 3)
                   3    2

          2
...
Warm-up
                         Divide.
              (3x + 2x − x + 3) ÷ (x − 3)
                   3    2

          2
...
Warm-up
                              Divide.
               (3x + 2x − x + 3) ÷ (x − 3)
                        3    2

 ...
Warm-up
                           Divide.
            (3x + 2x − x + 3) ÷ (x − 3)
                     3    2

     3x +1...
Warm-up
                           Divide.
            (3x + 2x − x + 3) ÷ (x − 3)
                     3    2

     3x +1...
Warm-up
                             Divide.
            (3x + 2x − x + 3) ÷ (x − 3)
                     3       2

     ...
Warm-up
                             Divide.
            (3x + 2x − x + 3) ÷ (x − 3)
                     3       2

     ...
Warm-up
                             Divide.
            (3x + 2x − x + 3) ÷ (x − 3)
                     3       2

     ...
Warm-up
                             Divide.
            (3x + 2x − x + 3) ÷ (x − 3)
                     3       2

     ...
Warm-up
                             Divide.
            (3x + 2x − x + 3) ÷ (x − 3)
                     3       2

     ...
Rational Roots Theorem
Rational Roots Theorem

  Let p be all factors of the leading
coefficient and q be all factors of the
 constant in any pol...
Synthetic Division
Synthetic Division


Another way to divide polynomials, without the
use of variables
Synthetic Division


Another way to divide polynomials, without the
use of variables

Only works if you’re dividing by a l...
Synthetic Division


Another way to divide polynomials, without the
use of variables

Only works if you’re dividing by a l...
Example 1
Determine whether 1 is a root of
       4x − 3x + x + 5
          6    4    2
Example 1
Determine whether 1 is a root of
       4x − 3x + x + 5
          6    4    2




   1 4 0 −3 0 1 0 5
Example 1
Determine whether 1 is a root of
       4x − 3x + x + 5
          6    4    2




   1 4 0 −3 0 1 0 5
Example 1
Determine whether 1 is a root of
         4x − 3x + x + 5
           6    4   2




   1 4 0 −3 0 1 0 5

     4
Example 1
Determine whether 1 is a root of
         4x − 3x + x + 5
           6    4   2




   1 4 0 −3 0 1 0 5

     4
Example 1
Determine whether 1 is a root of
       4x − 3x + x + 5
          6    4    2




   1 4 0 −3 0 1 0 5
       4
 ...
Example 1
Determine whether 1 is a root of
       4x − 3x + x + 5
          6    4    2




   1 4 0 −3 0 1 0 5
       4
 ...
Example 1
Determine whether 1 is a root of
       4x − 3x + x + 5
          6    4    2




   1 4 0 −3 0 1 0 5
       4 4...
Example 1
Determine whether 1 is a root of
       4x − 3x + x + 5
          6    4    2




   1 4 0 −3 0 1 0 5
       4 4...
Example 1
Determine whether 1 is a root of
       4x − 3x + x + 5
          6    4    2




   1 4 0 −3 0 1 0 5
       4 4...
Example 1
Determine whether 1 is a root of
       4x − 3x + x + 5
          6    4    2




   1 4 0 −3 0 1 0 5
       4 4...
Example 1
Determine whether 1 is a root of
       4x − 3x + x + 5
          6    4    2




   1 4 0 −3 0 1 0 5
       4 4...
Example 1
Determine whether 1 is a root of
       4x − 3x + x + 5
          6    4    2




   1 4 0 −3 0 1 0 5
       4 4...
Example 1
Determine whether 1 is a root of
       4x − 3x + x + 5
          6    4    2




   1 4 0 −3 0 1 0 5
       4 4...
Example 1
Determine whether 1 is a root of
       4x − 3x + x + 5
          6    4    2




   1 4 0 −3 0 1 0 5
       4 4...
Example 1
Determine whether 1 is a root of
       4x − 3x + x + 5
          6    4    2




   1 4 0 −3 0 1 0 5
       4 4...
Example 1
Determine whether 1 is a root of
       4x − 3x + x + 5
          6    4    2




   1 4 0 −3 0 1 0 5
       4 4...
Example 1
Determine whether 1 is a root of
       4x − 3x + x + 5
          6    4    2




   1 4 0 −3 0 1 0 5
       4 4...
Example 1
  Determine whether 1 is a root of
         4x − 3x + x + 5
             6       4       2




      1 4 0 −3 0 ...
Example 2
Use synthetic division to find the quotient and
                  remainder.
      (4x − 7x − 11x + 5) ÷ (4x − 5...
Example 2
Use synthetic division to find the quotient and
                  remainder.
      (4x − 7x − 11x + 5) ÷ (4x − 5...
Example 2
Use synthetic division to find the quotient and
                  remainder.
      (4x − 7x − 11x + 5) ÷ (4x − 5...
Example 2
Use synthetic division to find the quotient and
                  remainder.
      (4x − 7x − 11x + 5) ÷ (4x − 5...
Example 2
Use synthetic division to find the quotient and
                  remainder.
      (4x − 7x − 11x + 5) ÷ (4x − 5...
Example 2
Use synthetic division to find the quotient and
                  remainder.
      (4x − 7x − 11x + 5) ÷ (4x − 5...
Example 2
Use synthetic division to find the quotient and
                  remainder.
      (4x − 7x − 11x + 5) ÷ (4x − 5...
Example 2
Use synthetic division to find the quotient and
                  remainder.
      (4x − 7x − 11x + 5) ÷ (4x − 5...
Example 2
Use synthetic division to find the quotient and
                  remainder.
      (4x − 7x − 11x + 5) ÷ (4x − 5...
Example 2
Use synthetic division to find the quotient and
                  remainder.
      (4x − 7x − 11x + 5) ÷ (4x − 5...
Example 2
Use synthetic division to find the quotient and
                  remainder.
      (4x − 7x − 11x + 5) ÷ (4x − 5...
Example 3
Use synthetic division to find the quotient and
                  remainder.
       (6x − 16x + 17x − 6) ÷ (3x −...
Example 3
Use synthetic division to find the quotient and
                  remainder.
       (6x − 16x + 17x − 6) ÷ (3x −...
Example 3
Use synthetic division to find the quotient and
                  remainder.
       (6x − 16x + 17x − 6) ÷ (3x −...
Example 3
Use synthetic division to find the quotient and
                  remainder.
       (6x − 16x + 17x − 6) ÷ (3x −...
Example 3
Use synthetic division to find the quotient and
                  remainder.
       (6x − 16x + 17x − 6) ÷ (3x −...
Example 3
Use synthetic division to find the quotient and
                  remainder.
       (6x − 16x + 17x − 6) ÷ (3x −...
Example 3
Use synthetic division to find the quotient and
                  remainder.
       (6x − 16x + 17x − 6) ÷ (3x −...
Example 3
Use synthetic division to find the quotient and
                  remainder.
       (6x − 16x + 17x − 6) ÷ (3x −...
Example 3
Use synthetic division to find the quotient and
                  remainder.
       (6x − 16x + 17x − 6) ÷ (3x −...
Example 3
Use synthetic division to find the quotient and
                  remainder.
       (6x − 16x + 17x − 6) ÷ (3x −...
Example 3
Use synthetic division to find the quotient and
                  remainder.
       (6x − 16x + 17x − 6) ÷ (3x −...
Factoring a Quadratic
Factoring a Quadratic

Multiply a and c
Factoring a Quadratic

Multiply a and c

Factor ac into two factors that add up to b
Factoring a Quadratic

Multiply a and c

Factor ac into two factors that add up to b

Replace b with these two values
Factoring a Quadratic

Multiply a and c

Factor ac into two factors that add up to b

Replace b with these two values

Gro...
Factoring a Quadratic

Multiply a and c

Factor ac into two factors that add up to b

Replace b with these two values

Gro...
Factoring a Quadratic

Multiply a and c

Factor ac into two factors that add up to b

Replace b with these two values

Gro...
Example 4
                Factor.
a. 2x + x − 6
     2
                          b. 4x − 19x + 12
                        ...
Example 4
                Factor.
a. 2x + x − 6
     2
                          b. 4x − 19x + 12
                        ...
Example 4
                Factor.
a. 2x + x − 6
     2
                          b. 4x − 19x + 12
                        ...
Example 4
                Factor.
a. 2x + x − 6
     2
                          b. 4x − 19x + 12
                        ...
Example 4
                   Factor.
a. 2x + x − 6
      2
                             b. 4x − 19x + 12
                 ...
Example 4
                        Factor.
   a. 2x + x − 6
         2
                                  b. 4x − 19x + 12
 ...
Example 4
                        Factor.
   a. 2x + x − 6
         2
                                  b. 4x − 19x + 12
 ...
Example 4
                        Factor.
   a. 2x + x − 6
         2
                                  b. 4x − 19x + 12
 ...
Example 4
                        Factor.
   a. 2x + x − 6
         2
                                  b. 4x − 19x + 12
 ...
Example 4
                        Factor.
   a. 2x + x − 6
         2
                                  b. 4x − 19x + 12
 ...
Example 4
                        Factor.
   a. 2x + x − 6
         2
                                  b. 4x − 19x + 12
 ...
Example 4
                        Factor.
   a. 2x + x − 6
         2
                                  b. 4x − 19x + 12
 ...
Example 4
                        Factor.
   a. 2x + x − 6
         2
                                    b. 4x − 19x + 12...
Example 4
                        Factor.
   a. 2x + x − 6
         2
                                    b. 4x − 19x + 12...
Homework
Homework


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Synthetic Division

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Synthetic Division

  1. 1. Extra Section Synthetic Division Fo r us e w it h li nea r fact ors
  2. 2. Warm-up Divide. (3x + 2x − x + 3) ÷ (x − 3) 3 2
  3. 3. Warm-up Divide. (3x + 2x − x + 3) ÷ (x − 3) 3 2 x − 3 3x + 2x − x + 3 3 2
  4. 4. Warm-up Divide. (3x + 2x − x + 3) ÷ (x − 3) 3 2 2 3x x − 3 3x + 2x − x + 3 3 2
  5. 5. Warm-up Divide. (3x + 2x − x + 3) ÷ (x − 3) 3 2 2 3x x − 3 3x + 2x − x + 3 3 2 −(3x − 9x ) 3 2
  6. 6. Warm-up Divide. (3x + 2x − x + 3) ÷ (x − 3) 3 2 2 3x x − 3 3x + 2x − x + 3 3 2 −(3x − 9x ) 3 2 11x − x 2
  7. 7. Warm-up Divide. (3x + 2x − x + 3) ÷ (x − 3) 3 2 3x +11x 2 x − 3 3x + 2x − x + 3 3 2 −(3x − 9x ) 3 2 11x − x 2
  8. 8. Warm-up Divide. (3x + 2x − x + 3) ÷ (x − 3) 3 2 3x +11x 2 x − 3 3x + 2x − x + 3 3 2 −(3x − 9x ) 3 2 11x − x 2 −(11x − 33x) 2
  9. 9. Warm-up Divide. (3x + 2x − x + 3) ÷ (x − 3) 3 2 3x +11x 2 x − 3 3x + 2x − x + 3 3 2 −(3x − 9x ) 3 2 11x − x 2 −(11x − 33x) 2 32x + 3
  10. 10. Warm-up Divide. (3x + 2x − x + 3) ÷ (x − 3) 3 2 3x +11x +32 2 x − 3 3x + 2x − x + 3 3 2 −(3x − 9x ) 3 2 11x − x 2 −(11x − 33x) 2 32x + 3
  11. 11. Warm-up Divide. (3x + 2x − x + 3) ÷ (x − 3) 3 2 3x +11x +32 2 x − 3 3x + 2x − x + 3 3 2 −(3x − 9x ) 3 2 11x − x 2 −(11x − 33x) 2 32x + 3 −(32x − 96)
  12. 12. Warm-up Divide. (3x + 2x − x + 3) ÷ (x − 3) 3 2 3x +11x +32 2 x − 3 3x + 2x − x + 3 3 2 −(3x − 9x ) 3 2 11x − x 2 −(11x − 33x) 2 32x + 3 −(32x − 96) 99
  13. 13. Warm-up Divide. (3x + 2x − x + 3) ÷ (x − 3) 3 2 3x +11x +32 2 x − 3 3x + 2x − x + 3 3 2 −(3x − 9x ) 3 2 3x + 11x + 32, R : 99 2 11x − x 2 −(11x − 33x) 2 32x + 3 −(32x − 96) 99
  14. 14. Rational Roots Theorem
  15. 15. Rational Roots Theorem Let p be all factors of the leading coefficient and q be all factors of the constant in any polynomial. Then p/q gives all possible roots of the polynomial.
  16. 16. Synthetic Division
  17. 17. Synthetic Division Another way to divide polynomials, without the use of variables
  18. 18. Synthetic Division Another way to divide polynomials, without the use of variables Only works if you’re dividing by a linear factor
  19. 19. Synthetic Division Another way to divide polynomials, without the use of variables Only works if you’re dividing by a linear factor Allows for us to test whether a possible root is an actual zero
  20. 20. Example 1 Determine whether 1 is a root of 4x − 3x + x + 5 6 4 2
  21. 21. Example 1 Determine whether 1 is a root of 4x − 3x + x + 5 6 4 2 1 4 0 −3 0 1 0 5
  22. 22. Example 1 Determine whether 1 is a root of 4x − 3x + x + 5 6 4 2 1 4 0 −3 0 1 0 5
  23. 23. Example 1 Determine whether 1 is a root of 4x − 3x + x + 5 6 4 2 1 4 0 −3 0 1 0 5 4
  24. 24. Example 1 Determine whether 1 is a root of 4x − 3x + x + 5 6 4 2 1 4 0 −3 0 1 0 5 4
  25. 25. Example 1 Determine whether 1 is a root of 4x − 3x + x + 5 6 4 2 1 4 0 −3 0 1 0 5 4 4
  26. 26. Example 1 Determine whether 1 is a root of 4x − 3x + x + 5 6 4 2 1 4 0 −3 0 1 0 5 4 4 4
  27. 27. Example 1 Determine whether 1 is a root of 4x − 3x + x + 5 6 4 2 1 4 0 −3 0 1 0 5 4 4 4 4
  28. 28. Example 1 Determine whether 1 is a root of 4x − 3x + x + 5 6 4 2 1 4 0 −3 0 1 0 5 4 4 4 4 1
  29. 29. Example 1 Determine whether 1 is a root of 4x − 3x + x + 5 6 4 2 1 4 0 −3 0 1 0 5 4 4 1 4 4 1
  30. 30. Example 1 Determine whether 1 is a root of 4x − 3x + x + 5 6 4 2 1 4 0 −3 0 1 0 5 4 4 1 4 4 1 1
  31. 31. Example 1 Determine whether 1 is a root of 4x − 3x + x + 5 6 4 2 1 4 0 −3 0 1 0 5 4 4 1 1 4 4 1 1
  32. 32. Example 1 Determine whether 1 is a root of 4x − 3x + x + 5 6 4 2 1 4 0 −3 0 1 0 5 4 4 1 1 4 4 1 1 2
  33. 33. Example 1 Determine whether 1 is a root of 4x − 3x + x + 5 6 4 2 1 4 0 −3 0 1 0 5 4 4 1 1 2 4 4 1 1 2
  34. 34. Example 1 Determine whether 1 is a root of 4x − 3x + x + 5 6 4 2 1 4 0 −3 0 1 0 5 4 4 1 1 2 4 4 1 1 2 2
  35. 35. Example 1 Determine whether 1 is a root of 4x − 3x + x + 5 6 4 2 1 4 0 −3 0 1 0 5 4 4 1 1 2 2 4 4 1 1 2 2
  36. 36. Example 1 Determine whether 1 is a root of 4x − 3x + x + 5 6 4 2 1 4 0 −3 0 1 0 5 4 4 1 1 2 2 4 4 1 1 2 2 7
  37. 37. Example 1 Determine whether 1 is a root of 4x − 3x + x + 5 6 4 2 1 4 0 −3 0 1 0 5 4 4 1 1 2 2 4 4 1 1 2 2 7
  38. 38. Example 1 Determine whether 1 is a root of 4x − 3x + x + 5 6 4 2 1 4 0 −3 0 1 0 5 4 4 1 1 2 2 4 4 1 1 2 2 7 4x + 4x + x + x + 2x + 2, R : 7 5 4 3 2
  39. 39. Example 2 Use synthetic division to find the quotient and remainder. (4x − 7x − 11x + 5) ÷ (4x − 5) 3 2
  40. 40. Example 2 Use synthetic division to find the quotient and remainder. (4x − 7x − 11x + 5) ÷ (4x − 5) 3 2 5 4x − 5 → x − 4
  41. 41. Example 2 Use synthetic division to find the quotient and remainder. (4x − 7x − 11x + 5) ÷ (4x − 5) 3 2 5 4x − 5 → x − 4 5 4 4 −7 −11 5
  42. 42. Example 2 Use synthetic division to find the quotient and remainder. (4x − 7x − 11x + 5) ÷ (4x − 5) 3 2 5 4x − 5 → x − 4 5 4 4 −7 −11 5 4
  43. 43. Example 2 Use synthetic division to find the quotient and remainder. (4x − 7x − 11x + 5) ÷ (4x − 5) 3 2 5 4x − 5 → x − 4 5 4 4 −7 −11 5 5 4
  44. 44. Example 2 Use synthetic division to find the quotient and remainder. (4x − 7x − 11x + 5) ÷ (4x − 5) 3 2 5 4x − 5 → x − 4 5 4 4 −7 −11 5 5 4 -2
  45. 45. Example 2 Use synthetic division to find the quotient and remainder. (4x − 7x − 11x + 5) ÷ (4x − 5) 3 2 5 4x − 5 → x − 4 5 4 4 −7 −11 5 5 5 −2 4 -2
  46. 46. Example 2 Use synthetic division to find the quotient and remainder. (4x − 7x − 11x + 5) ÷ (4x − 5) 3 2 5 4x − 5 → x − 4 5 4 4 −7 −11 5 5 5 −2 27 4 -2 − 2
  47. 47. Example 2 Use synthetic division to find the quotient and remainder. (4x − 7x − 11x + 5) ÷ (4x − 5) 3 2 5 4x − 5 → x − 4 5 4 4 −7 −11 5 5 135 5 −2 − 8 27 4 -2 − 2
  48. 48. Example 2 Use synthetic division to find the quotient and remainder. (4x − 7x − 11x + 5) ÷ (4x − 5) 3 2 5 4x − 5 → x − 4 5 4 4 −7 −11 5 5 135 5 −2 − 8 27 95 4 -2 − 2 − 8
  49. 49. Example 2 Use synthetic division to find the quotient and remainder. (4x − 7x − 11x + 5) ÷ (4x − 5) 3 2 5 4x − 5 → x − 4 5 4 4 −7 −11 5 5 135 5 −2 − 8 27 95 4 -2 − 2 − 8 27 95 4x − 2x − 2 2 ,R:− 8
  50. 50. Example 3 Use synthetic division to find the quotient and remainder. (6x − 16x + 17x − 6) ÷ (3x − 2) 3 2
  51. 51. Example 3 Use synthetic division to find the quotient and remainder. (6x − 16x + 17x − 6) ÷ (3x − 2) 3 2 3x − 2 → x − 2 3
  52. 52. Example 3 Use synthetic division to find the quotient and remainder. (6x − 16x + 17x − 6) ÷ (3x − 2) 3 2 3x − 2 → x − 2 3 2 3 6 −16 17 −6
  53. 53. Example 3 Use synthetic division to find the quotient and remainder. (6x − 16x + 17x − 6) ÷ (3x − 2) 3 2 3x − 2 → x − 2 3 2 3 6 −16 17 −6 6
  54. 54. Example 3 Use synthetic division to find the quotient and remainder. (6x − 16x + 17x − 6) ÷ (3x − 2) 3 2 3x − 2 → x − 2 3 2 3 6 −16 17 −6 4 6
  55. 55. Example 3 Use synthetic division to find the quotient and remainder. (6x − 16x + 17x − 6) ÷ (3x − 2) 3 2 3x − 2 → x − 2 3 2 3 6 −16 17 −6 4 6 -12
  56. 56. Example 3 Use synthetic division to find the quotient and remainder. (6x − 16x + 17x − 6) ÷ (3x − 2) 3 2 3x − 2 → x − 2 3 2 3 6 −16 17 −6 4 -8 6 -12
  57. 57. Example 3 Use synthetic division to find the quotient and remainder. (6x − 16x + 17x − 6) ÷ (3x − 2) 3 2 3x − 2 → x − 2 3 2 3 6 −16 17 −6 4 -8 6 -12 9
  58. 58. Example 3 Use synthetic division to find the quotient and remainder. (6x − 16x + 17x − 6) ÷ (3x − 2) 3 2 3x − 2 → x − 2 3 2 3 6 −16 17 −6 4 -8 6 6 -12 9
  59. 59. Example 3 Use synthetic division to find the quotient and remainder. (6x − 16x + 17x − 6) ÷ (3x − 2) 3 2 3x − 2 → x − 2 3 2 3 6 −16 17 −6 4 -8 6 6 -12 9 0
  60. 60. Example 3 Use synthetic division to find the quotient and remainder. (6x − 16x + 17x − 6) ÷ (3x − 2) 3 2 3x − 2 → x − 2 3 2 3 6 −16 17 −6 4 -8 6 6 -12 9 0 6x − 12x + 9, R : 0 2
  61. 61. Factoring a Quadratic
  62. 62. Factoring a Quadratic Multiply a and c
  63. 63. Factoring a Quadratic Multiply a and c Factor ac into two factors that add up to b
  64. 64. Factoring a Quadratic Multiply a and c Factor ac into two factors that add up to b Replace b with these two values
  65. 65. Factoring a Quadratic Multiply a and c Factor ac into two factors that add up to b Replace b with these two values Group first 2 and last 2 terms
  66. 66. Factoring a Quadratic Multiply a and c Factor ac into two factors that add up to b Replace b with these two values Group first 2 and last 2 terms Factor out the GCF of each
  67. 67. Factoring a Quadratic Multiply a and c Factor ac into two factors that add up to b Replace b with these two values Group first 2 and last 2 terms Factor out the GCF of each Factors: (Stuff inside)(Stuff outside)
  68. 68. Example 4 Factor. a. 2x + x − 6 2 b. 4x − 19x + 12 2
  69. 69. Example 4 Factor. a. 2x + x − 6 2 b. 4x − 19x + 12 2 2i−6
  70. 70. Example 4 Factor. a. 2x + x − 6 2 b. 4x − 19x + 12 2 2i−6 = −12
  71. 71. Example 4 Factor. a. 2x + x − 6 2 b. 4x − 19x + 12 2 2i−6 = −12 = 4(−3)
  72. 72. Example 4 Factor. a. 2x + x − 6 2 b. 4x − 19x + 12 2 2i−6 = −12 = 4(−3) 2x + 4x − 3x − 6 2
  73. 73. Example 4 Factor. a. 2x + x − 6 2 b. 4x − 19x + 12 2 2i−6 = −12 = 4(−3) 2x + 4x − 3x − 6 2 (2x + 4x) + (−3x − 6) 2
  74. 74. Example 4 Factor. a. 2x + x − 6 2 b. 4x − 19x + 12 2 2i−6 = −12 = 4(−3) 2x + 4x − 3x − 6 2 (2x + 4x) + (−3x − 6) 2 2x(x + 2) − 3(x + 2)
  75. 75. Example 4 Factor. a. 2x + x − 6 2 b. 4x − 19x + 12 2 2i−6 = −12 = 4(−3) 2x + 4x − 3x − 6 2 (2x + 4x) + (−3x − 6) 2 2x(x + 2) − 3(x + 2) (x + 2)(2x − 3)
  76. 76. Example 4 Factor. a. 2x + x − 6 2 b. 4x − 19x + 12 2 2i−6 = −12 4i12 = 48 = 4(−3) 2x + 4x − 3x − 6 2 (2x + 4x) + (−3x − 6) 2 2x(x + 2) − 3(x + 2) (x + 2)(2x − 3)
  77. 77. Example 4 Factor. a. 2x + x − 6 2 b. 4x − 19x + 12 2 2i−6 = −12 4i12 = 48 = 4(−3) = (−16)(−3) 2x + 4x − 3x − 6 2 (2x + 4x) + (−3x − 6) 2 2x(x + 2) − 3(x + 2) (x + 2)(2x − 3)
  78. 78. Example 4 Factor. a. 2x + x − 6 2 b. 4x − 19x + 12 2 2i−6 = −12 4i12 = 48 = 4(−3) = (−16)(−3) 2x + 4x − 3x − 6 2 4x − 16x − 3x + 12 2 (2x + 4x) + (−3x − 6) 2 2x(x + 2) − 3(x + 2) (x + 2)(2x − 3)
  79. 79. Example 4 Factor. a. 2x + x − 6 2 b. 4x − 19x + 12 2 2i−6 = −12 4i12 = 48 = 4(−3) = (−16)(−3) 2x + 4x − 3x − 6 2 4x − 16x − 3x + 12 2 (2x + 4x) + (−3x − 6) 2 (4x − 16x) + (−3x + 12) 2 2x(x + 2) − 3(x + 2) (x + 2)(2x − 3)
  80. 80. Example 4 Factor. a. 2x + x − 6 2 b. 4x − 19x + 12 2 2i−6 = −12 4i12 = 48 = 4(−3) = (−16)(−3) 2x + 4x − 3x − 6 2 4x − 16x − 3x + 12 2 (2x + 4x) + (−3x − 6) 2 (4x − 16x) + (−3x + 12) 2 2x(x + 2) − 3(x + 2) 4x(x − 4) − 3(x − 4) (x + 2)(2x − 3)
  81. 81. Example 4 Factor. a. 2x + x − 6 2 b. 4x − 19x + 12 2 2i−6 = −12 4i12 = 48 = 4(−3) = (−16)(−3) 2x + 4x − 3x − 6 2 4x − 16x − 3x + 12 2 (2x + 4x) + (−3x − 6) 2 (4x − 16x) + (−3x + 12) 2 2x(x + 2) − 3(x + 2) 4x(x − 4) − 3(x − 4) (x + 2)(2x − 3) (x − 4)(4x − 3)
  82. 82. Homework
  83. 83. Homework Worksheet!

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