• Let $f(x)=x^7(x-1)^5(x+2)$. Find the zeros of $f$ and their multiplicities.

There are three different factors, but they occur multiple times.

From the factor $x$, we see that $x=0$ is a zero of multiplicity 7.

From the factor $x-1$, we see that $x=1$ is a zero of multiplicity 5.

From the factor $x+2$, we see that $x=-2$ is a zero of multiplicity 1.