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Created By : Rina Nayak

Reviewed By : Rajashekhar Valipishetty

Last Updated : May 16, 2023

Polynomial Remainder Theorem Calculator is an online tool that displays the remainder of a polynomial easily. All you have to do is provide the input values i.e dividend polynomial and divisor linear function and hit on the calculate button to get the output within no time.

Ex:

Remainder Theorem
by

### How to Solve Remainder of Polynomial Expressions Using Remainder Theorem?

Remainder Theorem is used that when a polynomial f(x) is divided by a linear factor in the form of x-a. Go through the following steps and use them while solving the remainder of a polynomial expression in fraction of seconds.

• Let us take polynomial f(x) as dividend and linear expression as divisor.
• The linear expression should be in the form of x-a.
• Then, the remainder value of polynomial will become f(a).
• So, substitute the c value in the polynomial expression and evaluate to get the remainder value.

### Remainder Theorem

In mathematics, the remainder theorem states that when a polynomial p(x) is divided by the linear factor x-a, then the remainder of the polynomial division is equal to p(a). General division formula is dividend = (divisor * quotient) + remainder Remainder theorem of a polynomial formula is p(x) = (x-a) * (q(x) + r(x) Where, p(x) is the dividend x-a is divisor q(x) is the quotient r(x) is the remainder.

Example

Question: Divide polynomial x²-3x+2 by the linear expression x+2 and find the remainder.

Solution:

Given values are

Given polynomial is f(x) = x²-3x+2

Linear expression is x+2

When x+2=0, then x=-2

Substitute x=-2 in f(x)

So, f(-2)=(-2)²-3(-2)+2

=4+6+2

The remainder of given polynomial is 3.

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### FAQs on Remainder Theorem Calculator

1. What is the remainder theorem formula?

If a polynomial f(x) is divided by the linear x - a, then the remainder of the polynomial expression is f(x) = (x-a) * q(x) + r(x). Where q(x) is the quotient, r(x) is the remainder.

2. How do you find the remainder theorem on a calculator?

You have to give the dividend polynomial and division linear function as inputs and click on the calculate button. It gives the remainder of the polynomial as output.

3. Is the factor theorem and remainder theorem the same?

According to the remainder theorem, a polynomial f(x) is divided by x-a gives the remainder as f(a). In the factor theorem, if "a" is the zero of a polynomial f(x) then x-a is the factor of f(x) or vice versa.

4. Can you use the remainder theorem If the remainder is zero?

The remainder of polynomial expressions becomes zero when it is divided by factor. You can use the polynomial remainder theorem at any case of polynomial function but the divisor must be a binomial in the form of x-a.