Question

I do not understand how to tell which one should be for which multiplicity

Answer 1

Given

$f(x)=8x^2(x-9)(x+5)^2$

To find the zeros of multiplicity one, multiplicity 2, multiplicity 3.

Now,

The zeros of multiplicity 1 are,

$\begin{gathered} x-9=0 \\ x=9 \end{gathered}$

The zeros of multiplicity 2 are,

$\begin{gathered} x=0 \\ x+5=0 \\ x=-5 \end{gathered}$

There are no zeros of multiplicity three since the polynomial has no factor to the power 3.