State division algorithm for polynomials.

The polynomial long division is an algorithm for dividing a polynomial by another polynomial of the same or lower degree; it is a generalized version of the familiar arithmetic technique called long division. It can be done manually because it separates a complex division problem into smaller ones.

Let’s take the Example:

f(x) and g(x) are two polynomials with,


Now we can find the polynomials p(x) and q(x) such that,

f(x) = p(x) × g(x) × q(x)

Where q(x) = 0 or degree of q(x) < is degree of g(x).

The result is;

Dividend = Quotient × Divisor + Remainder

This is known as the Division Algorithm for polynomials.