1. 8-5 Rational Zero Theorem
Objective:
To identify all possible rational zeros of a polynomial function by using the rational zero theorem.
To find zeros of polynomial functions.

2. Rational Zero Theorem

3. Corollary (Integral Zero Theorem)

4. Possible Rational Roots Exampleq p
Factors of p:
Factors of q:
Possible zeros:
(12 possible zeros)

5. Example 1 List all the possible rational zeros of these functions.
p(x) = 3x3 – 5x2 – 11x + 3

6. Example 2
List all the possible rational zeros of these functions and state whether they are positive or negative.
f(x) = 3x3 + 9x2 + x – 10
+ - i

7. Example 3 Find all the rational zeros for this function.
f(x) = x4 + 10x3 + 33x2 + 38x + 8
+ - i

8. Example 4 Find all the zeros for this function.
f(x) = x3 – 4x2 – 2x + 20
+ - i

9. Assignment
8-5 pg 513 #18-24 even 32, 34