PolynomialQuotientRemainder

PolynomialQuotientRemainder[p,q,x]

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

Details and Options

  • The remainder will always have a degree not greater than q.

Examples

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Basic Examples  (1)

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

Scope  (2)

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

PolynomialQuotientRemainder also works for rational functions:

Options  (1)

Modulus  (1)

Use a prime modulus:

Applications  (1)

Express the rational function as a polynomial and simple fraction:

The transformed rational function:

Properties & Relations  (2)

For a polynomial , :

Use Expand to verify identity:

PolynomialQuotient and PolynomialRemainder:

PolynomialReduce generalizes PolynomialQuotientRemainder for multivariate polynomials:

Introduced in 2007
 (6.0)