1. Warm Up: Solve & Sketch the graph:

2. Graphing Polynomials & Finding a Polynomial Function

3. Equivalent Statements: x = a is a zero of the function f. x = a is a solution of the polynomial equation f(x)=0. (x-a) is a factor of the polynomial f(x) (a, 0) is an x-intercept of the graph of f

4. Multiplicity

5. Repeated Zeros

6. Sketch the graph: Multiplicity of 2. Touches. Through these Points. End behavior:

7. Multiplicity - repeated zero – Means………….. If it occurs an odd number of times, the graph crosses the x-axis at the zero. If it occurs an even number of times, the graph will just touch the x-axis at the zero.

8. Sketch the graph: Mult. of 3 Goes Through Mult. Of 2 Touches 1 st Term would be End Behavior: 13 xy

9. Sketch the graph: Both have a multiplicity of 2. Just Touch! xy 1 st Term would be End Behavior:

10. Can you write a polynomial function if you know the zeros?

11. Find a Polynomial function that has the given zeros: 6, -3

12. Find a Polynomial function that has the given zeros: 0, 3, -5

13. Find a Polynomial function that has the given zeros: 3, 2, -2, -1

14. Find a Polynomial function that has the given zeros: and

15. Long & Synthetic Division

16. Use Long Division and use the result to factor the polynomial completely. 1 st Step:

17. 2 nd Step:

18. Divide using long division: Remainder

19. Divide using long division:

20. You Try: Divide using long division

21. Divide using long division

22. Synthetic Division

24. Divide using synthetic division to find the zeros:

25. Divide using synthetic division:

26. You Try: Divide using synthetic division – Find zeros: 4

27. You Try: Divide using synthetic division: