Polynomial Long Division

This calculator performs long division on two polynomials. It divides any polynomial by a polynomial of equal or lower degree. The calculator displays all steps on how the work was done.

Input dividend and divisor to find quotient and remainder.
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Input dividend and divisor $\left[ \dfrac{ \color{blue}{\text{dividend}} }{ \color{orange}{\text{divisor}} } \right]$

Dividend =

Divisor =

Examples:

(3x^2+3x-5)÷(x+2)

(2x^4-3x^2-x+2)÷(x^2+x-1)

Select what to compute

Divide the dividend by the divisor using long division

Find the remainder when dividend is divided by the divisor

Determine whether a divisor is a factor of the dividend

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Examples

ex 1:

Divide 3x²-4x+5 by x+2.

ex 2:

What is the remainder when 4x³-2x+11 is divided by x²+1?

ex 3:

Determine whether polynomial x-1 is a factor of x⁵+2x²-3x-4.

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Long Division Calculator

Find more worked-out examples in our database of solved problems.

TUTORIAL

How to calculate long division?

We can present long division algorithm with a simple example. Consider dividing the polynomial 3x²+4x-3 by x-3 using long division method. We can address this problem using a step-by-step approach.

Step 1: Identify the divisor and dividend and set up the division problem. In our example, the divisor is 3x²+4x-3, and the dividend is x-3. The division problem is:

_______________
x-3 | 3x^2+4x-3

Step 2:Divide the first term of a dividend 3x^2 by the first term of the divisor x.

      3x
_______________
x-3 | 3x^2+4x-3

Step 3:Multiply the divisor x-3 by the result from the last step (3x).

      3x
_______________
x-3 | 3x^2+4x-3
      3x^2-9x

Step 4:Subtract

      3x
_______________
x-3 | 3x^2+4x-3
      3x^2-9x
      _________
           13x-3

Step 5:Divide 13x by the first term of the divisor x.

      3x+13
_______________
x-3 | 3x^2+4x-3
      3x^2-9x
      _________
           13x-3

Step 6:Multiply

      3x+13
_______________
x-3 | 3x^2+4x-3
      3x^2-9x
      _________
           13x-3
           13x-39

Step 7:Subtract

      3x+13
_______________
x-3 | 3x^2+4x-3
      3x^2-9x
      _________
           13x-3
           13x-39
           -----
              36

Solution: The quotient is 3x+13 and the remainder is 36.

RESOURCES

1. Synthetic division calculator

2. Long division calculator for integers

3. Tutorial on how to perform polynomial long division

4. Solved long division example — video tutorial.

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