Given $ R=\Bbb Z/8 \Bbb Z$ , find a non-constant polynomial in $R[x]$ that is a unit

Question

I've been given $ R=\Bbb Z/8 \Bbb Z$ and asked to find a non-constant polynomial in $R[x]$ that is a unit.

Because units in $R[x]=$ units in $R$ and units in $R=\bar 1,\bar 3, \bar 5, \bar 7$, Would a polynomial with any of these units suffice? For example, if I let a polynomial in $ R=\Bbb Z/8 \Bbb Z$ be $f=\bar3x$, is $f$ a unit, or am I doing this wrong?

Thanks!

Answer 1

You have $(1+4x)(1-4x)=1$ in $\mathbb{Z}/8\mathbb{Z}$.