This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.1)

PolynomialRemainder

PolynomialRemainder
gives the remainder from dividing p by q, treated as polynomials in x.
  • The degree of the result in x is guaranteed to be smaller than the degree of q.
  • With the option Modulus->n, the remainder is computed modulo n.
Find the remainder after dividing one polynomial by another:
Find the remainder after dividing one polynomial by another:
In[1]:=
Click for copyable input
Out[1]=
The resulting polynomial will have coefficients that are rational expressions of input coefficients:
PolynomialRemainder also works for rational functions:
Use a prime modulus:
Euclid's algorithm for the greatest common divisor:
Divide by the leading coefficient:
For a polynomial , , where is given by PolynomialQuotient:
Use Expand to verify identity:
To get both quotient and remainder use PolynomialQuotientRemainder:
PolynomialReduce generalizes PolynomialRemainder for multivariate polynomials:
The variable assumed for the polynomials matters:
New in 1