Question

My teacher said this: "Please explain how you can tell if the multiplicity is odd or even. Then explain how you can tell if the multiplicity will be 1 or some odd number greater than 1." about some questions in my homework about graphing polynomials, can someone help me?

Answer 1

if a factor (x-h) occurs n times, it has a multiplicity of n.

Looking at the graph, if a root has odd multiplicity, the graph crosses the x-axis there. Think of y=x^3

If the multiplicity is even, the graph just touches the x-axis and turns back. Think of y=x^2

Answer 2

Take a look here for an example:

y = (x+2)^2 * (x-1)^3

http://www.wolframalpha.com/input/?i=(x%2B2)%5E2+*+(x-1)%5E3