I am confused by $A[x]$, I can't seem to grasp the concept. I saw this in a book and the proof was left as an exercise.
Any help would be much appreciated.
I know that if $B$ is a subring of $A$, then $B$ is closed under multiplication, addition and negatives.
In any ring $A, A[x]$ is the set of all the polynomials in $x$ whose coefficients are in $A$, with addition and multiplication of polynomials. But what is meant by "all the polynomials in $x$" ?