Let f(X)f(X) and g(X)g(X) be nonzero polynomials. Then there exist polynomials q(X)q(X) called the quotient and r(X)r(X) called the remainder such that:
(i) f(X)=q(X)g(X)+r(X)f(X)=q(X)g(X)+r(X) and
(ii) either r(X)=0r(X)=0 or the degree of r(X)r(X) is less than the degree of g(X)g(X).
To find q(X)q(X) and r(X)r(X), we use polynomial long division.