I am currently reading through the book Basic Commutative Algebra, by Balwant Singh, wherein the exercise I.XVI reads like:
Show that $(A[X])^\times=A^\times+nil(A[X])$.
Here, for a ring $A$, $A^\times$ means the set of all units, and $nil(A)$ is the intersection of all prime ideals, or the nilpotent radical, the radical of the zero ideal $(0)$.
P.S. I have shown that $A^\times=A^\times+nil A$, but cannot conquer this exercise.
Thanks for any help.