Rings and Fields- how to prove Z[x]/pZ[x] is an integral domain

[porroadventum]

Homework Statement

Prove Z[x]/pZ[x] is an integral domain where p is a prime natural number.

Homework Equations

I've seen in notes that this quotient ring can be isomorphic to (z/p)[x] and this is an integral domain but I don't know how to prove there is an isomorphism between them and how to prove it is an integral domain...

The Attempt at a Solution

 

[micromass]

Do you have any suggestion about what the isomorphism will be?? Just write down some map that looks intuitively right, most of the time this works.