Dividing Polynomials

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.