I'm studying abstract algebra and ran into the problem of solving equations where solutions are polynomials.
The problem is as follows: Given B a member of a polynomial field $F[x]$, having coefficients in field $F$. Find all the possible polynomials X in $F[x]$ where $X = B$. That is finding the tuples of coefficients that satisfy $X = B$.
What is not clear to me is how one defines the equation $X = B$: $X = B$ for all $x$ in $F$ or for at least one $x$?