# Ring homomorphism

## Homework Statement

$\mathbb{Z}[x]/(x^3-x) \rightarrow \mathbb{Z}$

Show that is ring homomorphism, and count the number of homomorphism..?

## The Attempt at a Solution

the map $f$ is homomorphism if,

$f(x+y)=f(x)+f(y)$
$f(xy)=f(x)f(y)$

I think, I must find a map for the question , but how should I choose the map, I don't know....