As with integers, operations related to division are key to many computations with polynomials. Mathematica
includes not only highly optimized univariate polynomial-division algorithms, but also state-of-the-art multivariate generalizations.
cancel factors in a ratio of polynomials
represent one polynomial as a sum of others
find a reduced Groebner basis for a list of polynomials
reduce polynomial coefficients modulo m
specify the modulus for a finite field