Polynomial Warm-Up: Long Division & Real Zeros Computation

1. Warm Up Compute the following by using long division. (You have 10 minutes and no calculators.) 1. 105/36 2. 210/ 82 3. 1956/ 15 4. 12350/ 27 5. 6239/ 18

2. 2.4 Real Zeros of Polynomial Functions

3. Division Algorithm for Polynomials

4. Remainder Theorem

5. Example Using Polynomial Long Division f(x) = x2 – 2x + 3 ÷ x – 1

6. Examples

7. Example Using the Remainder Theorem

8. Example Use the Remainder Theorem to find the remainder when f(x) is divided by x – k. f(x) = x4 – 5; k = 1

9. Example Evaluate the function at x = 1 f(1) = (1)4 – 5 = -4

10. Example Using Synthetic Division

11. Example Using Synthetic Division

12. Rational Zeros Theorem

13. Example Finding the Real Zeros of a Polynomial Function

14. Example Finding the Real Zeros of a Polynomial Function

15. Example Finding the Real Zeros of a Polynomial Function

16. Example Finding the Real Zeros of a Polynomial Function

17. Example Finding the Real Zeros of a Polynomial Function

18. Example Finding the Real Zeros of a Polynomial Function