# Abstract Algebra: a problem about ideal

## Homework Statement

Let J be the set of all polynomials with zero constant term in Z[x]. (Z=integers)
a.) Show that J is the principal ideal (x) in Z[x].
b.) Show that Z[x]/J consists of an infinite number of distinct cosets, one for each n$$\in$$Z.

## The Attempt at a Solution

I have trouble understanding what a principal ideal is. Any help on how I should start would be great. Thanks!

Dick