Division algorithm for Polynomial

Division algorithm for Polynomial

Let us consider two numbers a and b such that a is divisible by b then a is called is dividend, b is called the divisor and the resultant that we get on dividing a with b is called the quotient and here the remainder is zero, since a is divisible by b. Hence by division rule we can write,

Dividend = divisor x quotient + remainder.

This holds good even for polynomials too. Let f(x), g(x), q(x) and r(x) are polynomials then the division algorithm for polynomials states that “If f(x) and g(x) are two polynomials such that degree of f(x) is greater that degree of g(x) where g(x) ≠ 0, then there exists unique polynomials q(x) and r(x) such that f(x) = g(x).q(x) + r(x) where r(x) = 0 or degree of r(x) less than degree of g(x)”.