Let $J$ consist of all the polynomials $a_0+a_1x+...+a_nx^n$ in $A[x]$ where $A$ is a field, such that $a_0+a_1+a_2+...+a_n=0$. Prove tht $J$ is an ideal of $A[x]$.
So I know that a kernel is also the ideal, so I was wondering if $a_0+a_1+a_2+...+a_n=0$ then that would be the kernel (I believe). So since J includes the kernel then J is an ideal. Does this follow?