Chapter 8.3, Problem 9E

Let $F$ be a field. Prove that if $c\ne 0$ is a zero of $f(x)=a_0+a_{1}x+\mathrm{...}+a_n{x}^n\in F[x]$ then $c^{-1}$ is a zero of $a_n+a_{n-1}x+\mathrm{...}+a_0{x}^n.$