Notes On Division Algorithm for Polynomials - CBSE Class 10 Maths
Let f(x), g(x), q(x) and r(x) are polynomials then the division algorithm for polynomials states that â€œIf f(x) and g(x) are two polynomials such that degree of f(x) is greater than degree of g(x) where g(x) â‰  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) < degree of g(x). 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 it can written as, Dividend = divisor x quotient + remainder. This holds good even for polynomials too. Divide the highest degree term of the dividend by the highest degree term of the divisor and obtain the remainder. If the remainder is O or degree of remainder is less than divisor, then we cannot continue the division any furthur,if degree of remainder is equal to or more than divisor repeat the first step.

Summary

Let f(x), g(x), q(x) and r(x) are polynomials then the division algorithm for polynomials states that â€œIf f(x) and g(x) are two polynomials such that degree of f(x) is greater than degree of g(x) where g(x) â‰  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) < degree of g(x). 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 it can written as, Dividend = divisor x quotient + remainder. This holds good even for polynomials too. Divide the highest degree term of the dividend by the highest degree term of the divisor and obtain the remainder. If the remainder is O or degree of remainder is less than divisor, then we cannot continue the division any furthur,if degree of remainder is equal to or more than divisor repeat the first step.

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