let $\displaystyle \alpha$ be a zero of $\displaystyle f(x)=x^3+x^2+1$ over $\displaystyle \mathbb{Z}_{2}$, Show that $\displaystyle f(x)$ splits over $\displaystyle \mathbb{Z}_{2}(\alpha)$

I don't understand this question because$\displaystyle f(x)$ is irreducible in $\displaystyle \mathbb{Z}_{2}$ ($\displaystyle f(0)=1$ and $\displaystyle f(1)=1$) so how can $\displaystyle \alpha$ be its zero.