As with integers, operations related to division are key to many computations with polynomials. The Wolfram Language includes not only highly optimized univariate polynomial-division algorithms, but also state-of-the-art multivariate generalizations.

PolynomialQuotient  ▪  PolynomialRemainder  ▪  PolynomialQuotientRemainder

PolynomialGCD  ▪  PolynomialLCM  ▪  PolynomialExtendedGCD

SubresultantPolynomials  ▪  SubresultantPolynomialRemainders

Cancel — cancel factors in a ratio of polynomials

PolynomialReduce — represent one polynomial as a sum of others

GroebnerBasis — find a reduced Groebner basis for a list of polynomials

PolynomialMod — reduce polynomial coefficients modulo m

Modulus — specify the modulus for a finite field