1. Warm Up Compute the following by using long division.
(You have 10 minutes and no calculators.)
/36
/ 82
/ 15
/ 27
/ 18

2. Real Zeros of Polynomial Functions
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