# Remainder Theorem Calculator

**Remainder Theorem Calculator** calculates the remainder for the given polynomials. Remainder theorem enables us to calculate the remainder of the division of any polynomial by a linear polynomial, without actually carrying out the steps of the division algorithm.

## What is Remainder Theorem Calculator?

Remainder Theorem Calculator is an online tool that helps to calculate the remainder for the given polynomials. This online remainder theorem calculator helps you to calculate the remainder in a few seconds. To use this remainder theorem calculator, please enter the numerator and denominator in the given input box.

### Remainder Theorem Calculator

## How to Use Remainder Theorem Calculator?

Please follow the steps below to calculate the remainder using an online remainder theorem calculator:

**Step 1:**Go to online remainder theorem calculator.**Step 2:**Enter the polynomials in the given input box of the remainder theorem calculator.**Step 3:**Click on the**"Calculate"**button to calculate the remainder for the given polynomials.**Step 4:**Click on the**"Reset"**button to clear the field and enter the new polynomials.

## How Remainder Theorem Calculator Works?

The remainder theorem is stated as follows when a polynomial a(x) is divided by a linear polynomial b(x) (which is a polynomial of degree 1) whose zero is x = k, the remainder is given by r = a(k).

The general formula of the remainder theorem is Dividend = (Divisor × quotient) + remainder

p(x) = [(x - c) × q(x)] + r(x)

Let us understand this with the help of the following example.

**Solved Examples on Remainder Theorem Calculator**

**Example 1:**

Find the remainder when p(x) is 3x^{5 }- x^{4 }+ x^{3 }- 4x^{2 }+ 2 is divided by q(x) is x - 1 and verify it using the remainder theorem calculator?

**Solution:**

Given: Dividend p(x) = 3x^{5 }- x^{4 }+ x^{3 }- 4x^{2 }+ 2 and Divisor q(x) or linear factor = x - 1

To find the remainder, we will substitute the zero of q(x) into the polynomial p(x) to find the remainder r

Linear factor ,x - 1 = 0

x = 1

p(1) = 3(1)^{5 }- (1)^{4 }+ (1)^{3 }- 4(1)^{2 }+ 2

= 3 - 1 + 1 - 4 + 2

= 1

Therefore, the remainder is 1

**Example 2:**

Find the remainder when p(x) is x^{5 }- 2x^{4 }- 3x^{3 }+ 2x^{2 }+ 7 is divided by q(x) is x - 2 and verify it using the remainder theorem calculator?

**Solution:**

Given: Dividend p(x) = x^{5 }- 2x^{4 }- 3x^{3 }+ 2x^{2 }+ 7 and Divisor q(x) or linear factor = x - 2

To find the remainder, we will substitute the zero of q(x) into the polynomial p(x) to find the remainder r

Linear factor ,x - 2 = 0

x = 2

p(1) = (2)^{5 }- 2(2)^{4 }- 3(2)^{3 }+ 2(2)^{2 }+ 7

= 32 - 32 - 24 + 8 + 7

= -9

Therefore, the remainder is -9

Similarly, you can use the remainder theorem calculator and find the remainder for

- p(x) = x
^{2}+ 2x + 5 and q(x) = x - 1 - p(x) = 3x
^{3}- 2x^{2}+ 4x - 1 and q(x) = x + 5

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