# Homework Help: Polynomial Rings

1. Jan 23, 2012

### jgens

1. The problem statement, all variables and given/known data

Find eight elements $r \in \mathbb{Q}[x]/(x^4-16)$ such that $r^2=r$.

2. Relevant equations

N/A

3. The attempt at a solution

The elements $0+(x^4-16)$ and $1+(x^4-16)$ clearly satisfy the desired properties, but I still need six more elements. Can anyone help me figure out a technique for finding a few more elements?

Thanks!

2. Jan 23, 2012

### micromass

You can always brute force it. An arbitrary element in your ring has the form $[ax^3+bx^2+cx+d]$. Square it and see when the relation is satisfied.