1. Real Zeros of Polynomial Functions
Objective: Students will recall long and synthetic division of polynomial.

2. Long division
Do you remember how to divide two numbers by hand, including if there is a remainder? Do 3587 divided by 32

3. Polynomial Division
Do you remember how to divide a polynomial by a polynomial Try
(divisor)(quotient)+remainder=dividend
Divisor is what you are dividing the larger polynomial by
Remainder is what you can not divide into any more
Quotient is what in on top of the division box

4. Example

5. Remainder Theorem
If a polynomial f(x) is divided by x-k, then the remainder is r=f(k)

6. Example

7. Factor Theorem
A polynomial function f(x) has a factor x-k if and only if f(k)=0 Example c from before

8. Fundamental Connections

9. Synthetic Divsion
Keep Numbers just get rid of the variables

10. Example

11. Rational Zeros Theorem

12. Example

13. Example 2
You would then need to test all of these to determine which ones are zeros of the function

14. Homework
Pg 223 7,13,19,49,50,53