1. 2.5 Zeros of Polynomial Functions
The Rational Zero Theorem
Possible rational zeros =
Provides us with a list of all possible rational zeros of a polynomial function.
Factors of the constant
Factors of the l.c. 1

2. List all possible rational zeros of f(x) = x3 + 3x2 – 6x – 8
Example
List all possible rational zeros
of f(x) = x3 + 3x2 – 6x – 8
You try one
List all possible rational zeros
of f(x) = x3 + 2x2 – 5x – 6 2

3. List all possible rational zeros of f(x) = 3x4 – 11x3 – 3x2 – 6x + 8
Example
List all possible rational zeros
of f(x) = 3x4 – 11x3 – 3x2 – 6x + 8
You try one
List all possible rational zeros
of f(x) = 4x5 + 12x4 –x – 3 3

4. Combining the list with synthetic division will allow us to solve a function.
Example
Find all zeros
of f(x) = x3 – 2x2 – 11x + 12 4

5. You try one
Find all zeros
of f(x) = x3 + 8x2 + 11x – 20 5

6. P. 335 #1 – 15 odd 6