Home page for accesible maths Math 101 Chapter 1: Sequences and Series

Style control - access keys in brackets

Font (2 3) - + Letter spacing (4 5) - + Word spacing (6 7) - + Line spacing (8 9) - +

1.10 Division algorithm

Theorem (Division Algorithm)

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.