# What is the remainder when (x^{3} + 1) is divided by (x^{2} – x + 1)?

We will be using the long division method of the polynomial for finding the solution.

## Answer: The remainder is zero when (x^{3} + 1) is divided by (x^{2} – x + 1).

Let us see how we will use the long division method.

**Explanation**:

Using long division method: (x^{3 }+ 1) ÷ (x^{2 }- x + 1)

Multiply (x^{2 }- x + 1) by x and subtract from ( x^{3 }+ 1 )

= (x^{3 }+ 1) - (x^{2 }- x + 1) × (x)

= x^{3 }+ 1 - x^{3 }+ x^{2 }- x

= x^{2 }- x + 1

Multiply (x^{2 }- x + 1) by 1 and subtract from the remainder in first step.

= (x^{2 }- x + 1) - (x^{2 }- x + 1 )

= 0

There is no remainder left. That means (x^{3 }+ 1) is completetly divisible by (x^{2 }- x + 1)

You can see the image, how long division is performed:

Cuemath's online calculator helps you divide large polynomials and finds the quotient and the remainder