Question: Rem and Quo for multivariate polynomials

I am working with two multivariate functions A and B, with coefficients over a finite field. The x-degree of A is greater than or equal to B, which is greater than or equal to 1, and thus I want to find q and r such that:

A = q*B + r, where q, r are elements of K(y,z)[x], where K is my finite field. Obviously, I would like the x-degree of r to be less than that of B, and r not equal to 0.

My problem is this: the Rem and Quo commands, which will deal with my coefficients properly, don't do multivariate polynomials, while the evala(Rem()) command will work when the coefficients of x are multivariate polynomials, but over an algebraic number field rather than a finite field. Is there some command that I can use to do what I want, or should I just write a function to do it for me?

Thanks very much in advance - I apologize greatly if this question has been answered before, but I could not find a similar answer on this site.