1. Maximal ideal

Hi,

I've following homomorphism: $h:\mathbb{Z}[X] \rightarrow \mathbb{Z}$, $h(w)=w(0)$, where $w$ is a polynomial.
$\mathbox{ker}h$ - prime ideal but not maximal.

How can I find all maximal ideals?

Thanks for help.

2. You can start by noting that $M$ is maximal in your ring if and only if $\mathbb{Z}[X]/M$ is a field.