Question

Find the polynomial f(x) that has the roots of -2, 3 of multiplicity 2. Explain how you would verify the zeros of f(x)

Answer 1

If it were just -2 and 3, then the polynomial would be (x+2)(x-3). Remember the zero product property?

Answer 2

But each zero has multiplicity 2, which means its factor is squared.
So it would be x+2 squared times x-3 squared, or (x+2)^2 * (x-3) ^2.
Does that help?