What are the units of R[x]

I am studying for my abstract algebra midterm and I have completely forgotten what the units of R[x] where R is the ring of real numbers.

I am thinking that it is the units of R but I am thinking that R[x] could possibly be a field. I know R[x] has to be an integral domain but I don't know if I can say it is a field. Anything helps thanks

Let p(x) be a unit of R[x].
Then p(x) * q(x) = 1 for some q(x) in R[x].

Comparing degrees:
deg(p(x) q(x)) = deg 1
==> deg p(x) + deg q(x) = 0.
==> deg p(x) = deg q(x) = 0, since degrees are non-negative integers.

Hence, p(x) is constant (i.e., a real number).
However, we know that all nonzero real numbers are units.

Hence, U(R[x]) = R \ {0}, the nonzero real numbers.

I hope this helps!