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Math Calculators ▶ Remainder Theorem Calculator

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**Table of Content**

Remainder theorem calculator is free online tool that helps you to calculate the remainder of given polynomial expressions by remainder theorem.

Our factor theorem calculator provides step by step calculations of the factor of division. Here you can understand how to find the remainder of a polynomial using the formula.

In algebra, the remainder theorem or little Bezout’s theorem is an application of Euclidean division of different expressions, which is discovered by Etienne Bezout. It states when an expression is divided by a factor x-j, then the remainder of the division is equal to f(j).

When the polynomial f(x) is divisible by a linear factor of the form x-j, the theorem will be used by the remainder theorem calculator. If you want to do these calculations by hand, then follow the instructions below and use them to solve the rest of the polynomial expression in a couple of minutes.

- The polynomial f(x) is used as the dividend, and the linear expression is used as the divisor.
- The form of the linear expression must be x-j.
- Then, the remaining value of the polynomial becomes m(x).
- Therefore, insert the value of c into the polynomial and evaluate it to obtain the remainder value.

**Example**

Solve (x^4 + 12x^3 + 18x^2 – 9x + 22) with denominator (x – 4) using remainder theorem?

**Solution:**

Given values are

$$f(x) = x^4 + 12x^3 + 18x^2 – 9x + 22$$

x – 4 is in the form of x – (4).

Then c = 4

$$f(4) = (4)^4 + 12(4)^3 + 18(4)^2 – 9(4) + 22$$

$$= 256 + 768 + 288 – 36 + 22$$

$$= 1298$$

The remainder of given expression is 1298.

- First, enter the numerator polynomial.
- Then, substitute the denominator polynomial.
- Hit the “Calculate” button to see the remainder of the given expression.

The remainder calculator calculates:

- The remainder theorem calculator displays standard input and the outcomes.
- It provides all steps of the remainder theorem and substitutes the denominator polynomial in the given expression.
- You can find the remainder many times by clicking on the “Recalculate” button.

From the source of Wikipedia: Polynomial remainder theorem, little Bézout’s theorem, factor theorem.