Remainder Theorem Calculator

The Remainder Theorem Calculator is a free online available tool designed to make calculations simpler for you. It displays the quotient and the remainder for any given polynomial expression.

In traditional mathematics, the definition of remainder theorem states that when a given polynomial with function f(x) is divided by a linear factor x-a, then the remainder of that polynomial division is equal to f(a).

We also know that the dividend = (Divisor x Quotient) + Remainder

So, if f(x) is the dividend, (x-a) is divisor, q(x) is a quotient and r(x) is a remainder, then the function can be written as:

f(x) = (x-a) ·q(x) + r(x).  

Remainder Theorem is a specific approach of Euclidean division of polynomials. It is also coined as the little Bézout’s theorem.

Going by this theorem, if we divide a given polynomial P(x) by a factor of (x – a); which is not essentially an element of the polynomial, then you will find a smaller polynomial along with a remainder.

This remainder that has been obtained is actually a value of P(x) at x = a, more specifically P(a). So clearly, x – a is a divisor of P(x) if and only if P(a) = 0. 

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