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Remainder Theorem Calculator

Free handy Remainder Theorem Calculator tool displays the remainder of a difficult polynomial expression in no time. Simply provide the input divided polynomial and divisor polynomial in the mentioned input fields and tap on the calculate button to check the remainder of it easily and fastly.


Remainder Theorem

Here are some samples of Remainder Theorem calculations.

Remainder Theorem Calculator: If you are looking for a free online tool that does your math calculations and provides the remainder of a polynomial expressions? Then you are at the right place. To help you understand the remainder theorem concept we have listed everything in detail step by step. You will find each and every useful information like what is remainder theorem, solved examples.

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

When a polynomial function f(x) is divided by the linear x-c, then the remainder of polynomial function is always equal to f(c).

We know that Dividend = (Divisor x Quotient ) + Remainder

Then, f(x) = (x-c) * q(x) + r(x)

Where, f(x) is the polynomial function

x-c is the linear factor

q(x) quotient

r(x) is remainder.


Question: Solve (x^4 + 7x^3 + 5x^2 - 4x + 15) % (x + 2) using remainder theorem?


Given values are

f(x) = x^4 + 7x^3 + 5x^2 - 4x + 15

x + 2 is in the form of x - (-2).

Then c = -2

f(-2) = (-2)^4 + 7(-2)^3 + 5(-2)^2 - 4(-2) + 15

= 16 - 56 + 20 + 8 + 15

= 3.

The remainder of given polynomial is 3.

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Remainder Theorem Calculator

FAQs on Remainder Theorem Calculator

1. What are the different methods of solving remainder when a polynomial expression is divided by a linear factor?

We are having 3 methods to find the remainder of a polynomial divided by the linear factor. They are Polynomial Long Division, Synthetic Division or use Remainder Theorem.

2. Is Factor Theorem and Remainder Theorem same?

The factor theorem says that if a is a zero of a polynomial p(x), then x-a is the factor for p(x) or vice versa. The remainder theorem tells that for any polynomial p(x), divided by a x-a, the remainder is equal to the f(a).

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

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

4. What is the remainder for (2x^2 - 5x - 1) / (x - 3)?

Here, a = 3

f(x) = 2x^2 - 5x - 1

Then f(3) = 2 * 3^2 - 5(3) - 1

= 2 * 9 -15 - 1

= 2