Precalculus
posted by Melissa
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?

Steve
if a factor (xh) occurs n times, it has a multiplicity of n.
Looking at the graph, if a root has odd multiplicity, the graph crosses the xaxis there. Think of y=x^3
If the multiplicity is even, the graph just touches the xaxis and turns back. Think of y=x^2 
Steve
Take a look here for an example:
y = (x+2)^2 * (x1)^3
http://www.wolframalpha.com/input/?i=(x%2B2)%5E2+*+(x1)%5E3
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