Zeros and Multiplicity

Zeros and Multiplicity

Read each question carefully and answer to the best of your ability. Show all your work for full credit.

1. What is the multiplicity of the zero x = 2 in the polynomial function f(x) = (x - 2)^3 (x + 1)^2?

2. If a polynomial function has a zero with an even multiplicity, how does the graph behave at that x-intercept?

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

2. If a zero has an odd multiplicity, the graph of the polynomial will   the x-axis at that point.

3. The sum of the multiplicities of all real zeros of a polynomial is less than or equal to the   of the polynomial.

1. Find the zeros and their multiplicities for the polynomial function f(x) = x^4 - 2x^3 - 8x^2.

2. Describe the behavior of the graph of f(x) = (x + 3)(x - 1)^2 at each x-intercept.

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

2. If a polynomial function has a zero with multiplicity 1, the graph will have a local maximum or minimum at that zero.

Sketch a possible graph of a polynomial function with the following characteristics:

- Zeros at x = -2 (multiplicity 1), x = 0 (multiplicity 2), and x = 3 (multiplicity 3)