Polynomial long division

Summary

Polynomial long division is the algorithm that divides a polynomial $f$ by a polynomial $g$ with invertible leading coefficient. It produces the quotient $q$ and the remainder $r$ with $f = q g + r$ and $\deg r < \deg g$. These are the quotient and remainder of the division algorithm for polynomials. It is the basic step of the Euclidean algorithm for polynomials and of many computations in algebra.