Zeros and Multiplicity

Zeros and Multiplicity

Read each question carefully and provide thorough answers. Show all your work for full credit.

1. A zero of a polynomial function f(x) is a value 'c' such that f(c) =  .

2. The multiplicity of a zero is the number of times its corresponding   appears in the factored form of the polynomial.

3. If a zero has an even multiplicity, the graph of the function will   the x-axis at that zero.

4. If a zero has an odd multiplicity, the graph of the function will   through the x-axis at that zero.

5. For the polynomial function f(x) = (x - 2)^3 (x + 1)^2 (x - 5):

6. Write a polynomial function in factored form with the following characteristics:

- A zero at x = 3 with multiplicity 2

- A zero at x = -4 with multiplicity 1

- A zero at x = 0 with multiplicity 3

7. If the graph of a polynomial function touches the x-axis at x = -2 and turns around, what can be inferred about the multiplicity of the zero at x = -2?

8. Describe the end behavior and the behavior at each zero for the function f(x) = -(x + 3)(x - 1)^2.

9. A polynomial function can have more zeros than its degree.

10. The multiplicity of a zero affects the number of x-intercepts of the graph.

11. If a polynomial function has zeros at x = -1 (multiplicity 3), x = 2 (multiplicity 1), and x = 4 (multiplicity 2), describe what happens to the graph at each of these zeros.