1. Polynomials and Rational Functions By Lane Gonzalez, Alexus Brown, Helena Chevalier

2. Polynomial Degree Where n is a nonnegative integer and The numbers are called the coefficients of the polynomial is the constant term is the leading coefficient.

3. Finding rational zeros Finding the real zeros of a polynomial can be done by: –factoring the polynomial algebraically –Using the Rational Zeros Theorem/Quadratic Formula –Graphing the Function

4. Algebraically Factor! Rational Zeros! THAT WAS FUN!!

5. Finding Real Zeros List possible zeros Divide Repeat

6. List all possible zeros P/Q= Factors of P divided by Factors of Q Simplify

7. Substituting and Dividing Substitute possible zeros one at a time. 1 is not a zero of “f” 2 is a zero of “f” Now synthetically divide by 2 (see board)

8. Using the quadratic formula for each part of the now factored equation, the zeros are: Finding Complex Zeros

9. End Behavior End behavior is determined by the degree of the leading coefficient If it has odd degree

10. Dividing Polynomials Dividing polynomials is a lot like dividing numbers See Board

11. Graphing Polynomial Functions To graph a polynomial function –F–Find the zeros –G–Get some test points –D–Determine end behavior –G–Graph

12. Example X=0,3,-1

13. Example cont. x f(x) -3 -20 -2 0 6 0 4 1 0 3/2 -7/8 2 0 3 10 Graph on calculator now!

14. Graphing Rational Functions Most easily done by putting directly into calculator Example: f(x)=1/x