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Mathematica > Mathematics and Algorithms > Polynomial Algebra > Polynomial Division >

Built-in Mathematica Symbol

PolynomialQuotientRemainder

PolynomialQuotientRemainder[p, q, x]
gives a list of the quotient and remainder of p and q, treated as polynomials in x.

Find the quotient and remainder after dividing one polynomial by another:

The resulting polynomial will have coefficients that are rational expressions of input coefficients:

PolynomialQuotientRemainder also works for rational functions:

Use a prime modulus:

Express the rational function as a polynomial and simple fraction:

The transformed rational function:

For a polynomial f, f

q g+r:

Use Expand to verify identity: