Chapter 8.3, Problem 5E

Let $F$ be a field and $f(x)=a_0+a_{1}x+\mathrm{...}+a_n{x}^n\in F[x].$

Prove that $x-1$ is a factor of $f(x)$ if and only if $a_0+a_1+\mathrm{...}+a_n=0.$

Prove that $x+1$ is a factor of $f(x)$ if and only if $a_0+a_1+\mathrm{...}+{(-1)}^n{a}_n=0.$