Remainder Theorem Calculator


Remainder Theorem Calculator is a free online tool that displays the quotient and remainder for the given polynomial expression. 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 for the polynomial when 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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