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Dividing Polynomials

Dividing Polynomials. Synthetic Division Used to factor polynomials and find the roots / zeros. Synthetic Division. Same idea as synthetic substitution. Remember to use 0 as the coefficient of any missing terms!. Synthetic Division. Divide f(x) = x 3 – x + 1 by x + 2.

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Dividing Polynomials

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  1. Dividing Polynomials Synthetic Division Used to factor polynomials and find the roots / zeros.

  2. Synthetic Division Same idea as synthetic substitution. Remember to use 0 as the coefficient of any missing terms!

  3. Synthetic Division Divide f(x) = x3 – x + 1 by x + 2. Same idea as synthetic substitution. Remember to use 0 as the coefficient of any missing terms!

  4. Synthetic Division Divide f(x) = x3 – x + 1 by x + 2. Same idea as synthetic substitution. Remember to use 0 as the coefficient of any missing terms!

  5. Synthetic Division Divide f(x) = x3 – x + 1 by x + 2. Same idea as synthetic substitution. Remember to use 0 as the coefficient of any missing terms!

  6. Synthetic Division Divide f(x) = x3 – x + 1 by x + 2. Same idea as synthetic substitution. Remember to use 0 as the coefficient of any missing terms!

  7. Synthetic Division Divide f(x) = x3 – x + 1 by x + 2. Same idea as synthetic substitution. Remember to use 0 as the coefficient of any missing terms!

  8. Synthetic Division Divide f(x) = x3 – x + 1 by x + 2. Same idea as synthetic substitution. Remember to use 0 as the coefficient of any missing terms!

  9. Synthetic Division Divide f(x) = x3 – x + 1 by x + 2. Same idea as synthetic substitution. Remember to use 0 as the coefficient of any missing terms!

  10. Synthetic Division Divide f(x) = x3 – x + 1 by x + 2. Same idea as synthetic substitution. Remember to use 0 as the coefficient of any missing terms!

  11. Synthetic Division Divide f(x) = x3 – x + 1 by x + 2. Same idea as synthetic substitution. Remember to use 0 as the coefficient of any missing terms!

  12. Synthetic Division Divide f(x) = x3 – x + 1 by x + 2. Same idea as synthetic substitution. Remember to use 0 as the coefficient of any missing terms! remainder constant x x2

  13. Synthetic Division Divide f(x) = x3 – x + 1 by x + 2. Same idea as synthetic substitution. Remember to use 0 as the coefficient of any missing terms! remainder constant x x2

  14. Factoring Use one factor to divide the polynomial and find the rest.

  15. Completely factor f(x) = x3 – 10x2 + 19x + 30 given that f(6) = 0. Factoring Use one factor to divide the polynomial and find the rest.

  16. Completely factor f(x) = x3 – 10x2 + 19x + 30 given that f(6) = 0. Factoring First, divide f(x) = x3 – 10x2 + 19x + 30 by x – 6. Use one factor to divide the polynomial and find the rest.

  17. Completely factor f(x) = x3 – 10x2 + 19x + 30 given that f(6) = 0. Factoring First, divide f(x) = x3 – 10x2 + 19x + 30 by x – 6. Use one factor to divide the polynomial and find the rest.

  18. Completely factor f(x) = x3 – 10x2 + 19x + 30 given that f(6) = 0. Factoring First, divide f(x) = x3 – 10x2 + 19x + 30 by x – 6. Use one factor to divide the polynomial and find the rest. x2 – 4x – 5

  19. Completely factor f(x) = x3 – 10x2 + 19x + 30 given that f(6) = 0. Factoring First, divide f(x) = x3 – 10x2 + 19x + 30 by x – 6. Use one factor to divide the polynomial and find the rest. x2 – 4x – 5 Second, factor the binomial x2 – 4x – 5.

  20. Completely factor f(x) = x3 – 10x2 + 19x + 30 given that f(6) = 0. Factoring First, divide f(x) = x3 – 10x2 + 19x + 30 by x – 6. Use one factor to divide the polynomial and find the rest. x2 – 4x – 5 Second, factor the binomial x2 – 4x – 5. x2 – 4x – 5 = (x – 5)(x + 1)

  21. Completely factor f(x) = x3 – 10x2 + 19x + 30 given that f(6) = 0. Factoring First, divide f(x) = x3 – 10x2 + 19x + 30 by x – 6. Use one factor to divide the polynomial and find the rest. x2 – 4x – 5 Second, factor the binomial x2 – 4x – 5. x2 – 4x – 5 = (x – 5)(x + 1) So f(x) = (x – 6)(x – 5)(x + 1).

  22. Practice Use synthetic division to completely factor f(x) = x3 – 10x2 + 8x + 64 given that f(-2) = 0.

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