Remainder Theorem Calculator


Remainder Theorem Calculator is a free online tool that displays the quotient and remainder of division for the given polynomial expressions. BYJU’S online remainder theorem calculator tool makes the calculation faster, and it displays the result in a fraction of seconds.

How to Use the Remainder Theorem Calculator?

The procedure to use the remainder theorem calculator is as follows:
Step 1: Enter the numerator and denominator polynomial in the respective input field
Step 2: Now click the button “Divide” to get the output
Step 3: Finally, the quotient and remainder will be displayed in the new window

What is the Remainder Theorem?

In mathematics, a remainder theorem states that when a polynomial f(x) is divided by a linear factor x-a, then the remainder of the polynomial division is equal to f(a).
We know that, Dividend = (Divisor x Quotient ) + Remainder
If f(x) is a divident, (x-a) is divisor, q(x) is a quotient, r(x) is a remainder,
It can be written as:
f(x) = (x-a)·q(x) + r(x)

Example

Question:
Determine the remainder when the polynomial 3x2-1 is divided by x-1.
Solution:
Given: Dividend = 3x2-1
Divisor = x-1
We know that,
f(x) = (x-a)·q(x) + r(x)
When 3x2-1 is divided by x-1, we get the quotient 3x+3, and remainder 2.

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