Everything looks good except (c). You are missing a lot of units. For example, what about ? It has an inverse: .
I am not sure exactly what this question is asking:
Determine the following groups of units:
a) U(Z[x]) where Z[x] is all polynomials with integer coefficients
b) U(Z[i]) where Z[i] is the gaussian integers (a+bi)
c) U(R[x]) where R[x] is all polynomials with real coefficients
I think this means find which elements in these groups have inverses
I am not quite sure but I have: