1. Chapter 3 3.2 Polynomials of Higher Degree
Obj – identify the end behaviors and zeros in order to graph a polynomial
3.3 Remainder and Factor Theorems
Obj – use the synthetic formula to divide polynomial functions

2. 3.2 Polynomials of Higher Degree
Review: Degree = 0 y = c Degree = 1 y = mx + b Degree = 2 y =

3. Polynomials of Higher Degree
Degree = 3 Degree = 4 Degree = 5 Degree = 6

4. Summarize If the degree is even, the end behaviors . . .
If the degree is odd, the end behaviors . . .
If the leading coefficient is positive, the right end behavior . . .
If the leading coefficient is negative, the right end behavior . . .

5. Practice
Determine the end behaviors.

6. Real Zeros of a Function
Factor to find the real zeros. Real zeros are also the x-intercepts of the graph of the function. Use the end behaviors and the zeros to sketch the graph of the function.

7. Even and Odd Powers of (x-c) Theorem
Use the graphing calculator to graph the polynomial Remember that the factors give the zeros or x-intercepts. If the power of the factor is odd, the graph If the power of the factor is even, the graph . . .

8. Putting It All Together
Sketch the graph of
Factor to find the zeros.
Find the y-intercept.
Determine the end behaviors.
Sketch.

9. 3.3 Division of Polynomials
Long Division or Synthetic Division
Review:

10. Use the same process with polynomials.
Divide Polynomials
Use the same process with polynomials.

11. Synthetic Division
Another process to divide polynomials IF you are dividing by a polynomial of form x – c. Rewrite:

12. Practice
Divide: Solve given that 2 is a zero.

13. The Remainder Theorem
If a polynomial P(x) is divided by x – c, then the remainder equals P(c). Use synthetic division. The remainder is P(c).

14. The Factor Theorem
A polynomial function P(x) has a factor (x – c) if and only if P(c) = 0. Determine whether the given binomial is a factor of P(x). Use synthetic division. If the remainder is zero, the binomial is a factor. Otherwise, the binomial is not a factor.

15. Assignment
– 30 by 5, 45 – 60 by 5,
, 5, 9, 17, 21, 25, 33, 37, 41