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Polynomial Long Division Calculator

Maya Lin-Takahashi • Oct 3, 2026 • 9 min read

Polynomial Long Division Calculator

Polynomial Long Division Calculator

Eevaluate the expression below:

2x⁷ + 3x⁶ - 6x⁵ + 6x⁴ - 2x³ - 8x² + 6x - 1

x² - 1

Setup long division format

Step 1
1a) Divide 2x⁷ ÷ x²
2x⁷ ÷ x² = 2x^{(7 - 2)} = 2x⁵

1b) Multiply 1a by the divisor
2x⁵(x² - 1) = 2x⁷ - 2x⁵
Click here to see the Math for this Multiplication.

1c) Subtract 2x⁷ - 2x⁵
Click here to see the Math.

2x⁵

x²

-

1

2x⁷

+

3x⁶

-

6x⁵

+

6x⁴

-

2x³

-

8x²

+

6x

-

1

2x⁷

-

2x⁵

3x⁶

-

4x⁵

+

6x⁴

-

2x³

-

8x²

+

6x

-

1

Step 2
2a) Divide 3x⁶ ÷ x²
3x⁶ ÷ x² = 3x^{(6 - 2)} = 3x⁴

2b) Multiply 2a by the divisor
3x⁴(x² - 1) = 3x⁶ - 3x⁴
Click here to see the Math for this Multiplication.

2c) Subtract 3x⁶ - 3x⁴
Click here to see the Math.

2x⁵

+

3x⁴

x²

-

1

2x⁷

+

3x⁶

-

6x⁵

+

6x⁴

-

2x³

-

8x²

+

6x

-

1

2x⁷

-

2x⁵

3x⁶

-

4x⁵

+

6x⁴

-

2x³

-

8x²

+

6x

-

1

3x⁶

-

3x⁴

-4x⁵

+

9x⁴

-

2x³

-

8x²

+

6x

-

1

Step 3
3a) Divide -4x⁵ ÷ x²
-4x⁵ ÷ x² = -4x^{(5 - 2)} = -4x³

3b) Multiply 3a by the divisor
-4x³(x² - 1) = -4x⁵ + 4x³
Click here to see the Math for this Multiplication.

3c) Subtract -4x⁵ + 4x³
Click here to see the Math.

2x⁵

+

3x⁴

-

4x³

x²

-

1

2x⁷

+

3x⁶

-

6x⁵

+

6x⁴

-

2x³

-

8x²

+

6x

-

1

2x⁷

-

2x⁵

3x⁶

-

4x⁵

+

6x⁴

-

2x³

-

8x²

+

6x

-

1

3x⁶

-

3x⁴

-4x⁵

+

9x⁴

-

2x³

-

8x²

+

6x

-

1

-4x⁵

+

4x³

9x⁴

-

6x³

-

8x²

+

6x

-

1

Step 4
4a) Divide 9x⁴ ÷ x²
9x⁴ ÷ x² = 9x^{(4 - 2)} = 9x²

4b) Multiply 4a by the divisor
9x²(x² - 1) = 9x⁴ - 9x²
Click here to see the Math for this Multiplication.

4c) Subtract 9x⁴ - 9x²
Click here to see the Math.

2x⁵

+

3x⁴

-

4x³

+

9x²

x²

-

1

2x⁷

+

3x⁶

-

6x⁵

+

6x⁴

-

2x³

-

8x²

+

6x

-

1

2x⁷

-

2x⁵

3x⁶

-

4x⁵

+

6x⁴

-

2x³

-

8x²

+

6x

-

1

3x⁶

-

3x⁴

-4x⁵

+

9x⁴

-

2x³

-

8x²

+

6x

-

1

-4x⁵

+

4x³

9x⁴

-

6x³

-

8x²

+

6x

-

1

9x⁴

-

9x²

-6x³

+

x²

+

6x

-

1

Step 5
5a) Divide -6x³ ÷ x²
-6x³ ÷ x² = -6x^{(3 - 2)} = -6x

5b) Multiply 5a by the divisor
-6x(x² - 1) = -6x³ + 6x
Click here to see the Math for this Multiplication.

5c) Subtract -6x³ + 6x
Click here to see the Math.

2x⁵

+

3x⁴

-

4x³

+

9x²

-

6x

x²

-

1

2x⁷

+

3x⁶

-

6x⁵

+

6x⁴

-

2x³

-

8x²

+

6x

-

1

2x⁷

-

2x⁵

3x⁶

-

4x⁵

+

6x⁴

-

2x³

-

8x²

+

6x

-

1

3x⁶

-

3x⁴

-4x⁵

+

9x⁴

-

2x³

-

8x²

+

6x

-

1

-4x⁵

+

4x³

9x⁴

-

6x³

-

8x²

+

6x

-

1

9x⁴

-

9x²

-6x³

+

x²

+

6x

-

1

-6x³

+

6x

x²

-

1

Step 6
6a) Divide x² ÷ x²
x² ÷ x² = 1x^{(2 - 2)} = 1

6b) Multiply 6a by the divisor
1(x² - 1) = x² - 1
Click here to see the Math for this Multiplication.

6c) Subtract x² - 1
Click here to see the Math.

2x⁵

+

3x⁴

-

4x³

+

9x²

-

6x

+

1

x²

-

1

2x⁷

+

3x⁶

-

6x⁵

+

6x⁴

-

2x³

-

8x²

+

6x

-

1

2x⁷

-

2x⁵

3x⁶

-

4x⁵

+

6x⁴

-

2x³

-

8x²

+

6x

-

1

3x⁶

-

3x⁴

-4x⁵

+

9x⁴

-

2x³

-

8x²

+

6x

-

1

-4x⁵

+

4x³

9x⁴

-

6x³

-

8x²

+

6x

-

1

9x⁴

-

9x²

-6x³

+

x²

+

6x

-

1

-6x³

+

6x

x²

-

1

x²

-

1

We have no remainder:

2x⁵ + 3x⁴ - 4x³ + 9x² - 6x + 1

You have 1 free calculations remaining

What is the Answer?

2x⁵ + 3x⁴ - 4x³ + 9x² - 6x + 1

How does the Polynomial Long Division Calculator work?

Free Polynomial Long Division Calculator - Polynomial Long Division Calculator
This calculator has 2 inputs.

What 3 formulas are used for the Polynomial Long Division Calculator?

Divide the first term of the dividend by the first term of the divisor
We multiply that part of the quotient by the divisor
Subtract Step 2 from our main polynomial.

For more math formulas, check out our Formula Dossier

What 2 concepts are covered in the Polynomial Long Division Calculator?

division: separate a number into parts
polynomial long division: an algorithm for dividing a polynomial by another polynomial of the same or lower degree

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Author

Maya Lin-Takahashi

Maya is a hardware enthusiast who tests and reviews smart home devices, smartphones, wearables, and audio gear. She focuses on practical consumer value and build quality.