Question

A polynomial function has a root of –3 with multiplicity 2, a root of 0 with multiplicity 1, a root of 1 with multiplicity 1, and a root of 3 with multiplicity 2. If the function has a positive leading coefficient and is of even degree, which could be the graph of the function?​

Answer 1

We are given a polynomial function has :
A root of –3 (multiplicity 2).
Therefore, one factor would be (x+3)^2
A root of 0 with multiplicity 1.
Therefore another factor is x.
A root of 1 with multiplicity 1.
Therefore another factor is (x-1).
A root of 3 with multiplicity 2.
Therefore, another factor would be (x-3)^2
Therefore, polynomial function would