Elliptic Curves over $F_{p^2}$

Question

For a finite field $F_{p^2}$, polynomial elements appear. For example, $F_{2^2}=\{0,1,x,x+1\}$.

Now when defining an Elliptic Curve $E:y^2=x^3+Ax+B$ over a field of the form $F_{p^2}$.

Does this mean that $A$ and $B$ can be polynomials??