Are Units in R[x] Exactly the Same as Units in R When R is an Integral Domain?

[mathmajor2013]

Question: Show that if R is an integral domain then R^x=R[x]^x(or that the units in R[x] are precisely the units in R, but viewed as constant polynomials).

 

[Landau]

This is pretty straight-forward. What have you tried?

 

[Tom Gilroy]

Well, what happens when we multiply any non-constant polynomial in R[x] by any non-zero polynomial in R[x]?

 

[mathwonk]

could use concept of degree.