Find a nontrivial unit polynomial in $\mathbb Z_4[x]$ Find a unit $p(x)$ in $\mathbb{Z}_4[x]$ such that $\deg p(x)>1$
What I know:
A unit has an inverse that when the unit is multiplied by the inverse we get the identity element.
But I am confused by the concept of degree
"If $n$ is the largest nonnegative number
for which an $a_n \neq 0$, we say that the degree of $f$ is $n$."
So I am looking for a polynomial in $\mathbb{Z}_4[x]$ that has an inverse..
Also I am not sure exactly what is $\mathbb{Z}_4[x]$?
Any ideas on how to get started on this problem?

Take $p(x) = 2x^2+1$. Observe that $p(x)^2 = (2x^2+1)^2 = 4x^4+4x^2+1 = 1$, and $p(x)$ has degree $2$.
