Polynomial Long Division Calculator

The Polynomial long division calculator with steps is used for the division of one polynomial equation by another. Dividing polynomials is difficult but this calculator makes it easy.

Polynomial Long Division

Synthetic Division Calculation for 4th Degree Polynomials

  • x
  • Devided By:

  • x     +  
  • 5x³ + 7x² + 5x¹ + 8x 3x + 5

The dividend can be a polynomial of up to 4 degrees and the divisor can be of the order of 2.

How to use a polynomial long division calculator?

Follow the instructions below.

  1. Enter the coefficients of the variables of the dividend.
  2. Enter the coefficients of the divisor.
  3. Click calculate.

If the polynomial equation you have is of order 3 or less than it then simply input zero (0) as the coefficient of the variable x4. Also, enter the negative sign carefully.

What are polynomial equations?

The polynomials are expressions that consist of both variables and digits. E.g 3x3 - 2x2 + 1. These expressions are particularly difficult to solve.

How to divide polynomials?

The process of dividing polynomials is long and complex. This is why it is called polynomial long division. Use the polynomial long division calculator above to divide polynomials. 

Below you can see a solved example of polynomial long division.


Divide 4x - 3x2 + 2 - 3x by 3x.

Step 1: Identify the dividend and divisor.

Dividend = - 4x2 + 3x3 + 2 - 3x
Divisor = 3x

Step 2:  Arrange the polynomial equation of dividend.

= - 4x2 + 3x3 + 2 - 3x
=  3x3 - 4x2 - 3x + 2

Step 3: Place the values in the long division symbol and solve.

Multiply 3x by x2 and to get 3x3. Now, take it as a coefficient.

Next, multiply 3x by -4x/3. It will be -12x2/3 and eventually -4x2.

Now, multiply the divisor again by -1.

Hence the quotient is x2-4x/3-1 with a remainder of 2. It will be written in the form of mixed numbers as:

And this is the final answer.


  1. Polynomial equation - properties, techniques, and examples | storyofmathematics.com
  2. Dividing polynomials | math-from-scratch.com