Polynomial Long Division Calculator

Perform the long division of polynomials step by step

The calculator will perform the long division of polynomials, with steps shown.

Related calculators: Synthetic Division Calculator, Long Division Calculator

Divide (dividend):

By (divisor):

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

Master the division of polynomials with our robust Polynomial Long Division Calculator! Unlike simple arithmetic, polynomial long division requires complex rules and steps that can be challenging and laborious to handle manually. This is precisely where our calculator comes into play. Built for precision and speed, it swiftly generates accurate solutions, supplemented by in-depth, step-by-step procedures to navigate you through the process.

How to Use the Polynomial Long Division Calculator?

  • Input

    Start by typing or pasting the polynomial you wish to divide in the appropriate input field. Next, input the polynomial by which you want to divide.

  • Calculation

    Once you enter the dividend and divisor, click the "Calculate" button.

  • Result

    The calculator will promptly display the solution, including a step-by-step breakdown of the division process, making it easier to understand the calculation.

What Is Polynomial Long Division?

Polynomial long division is an algebraic method for dividing one polynomial by another of the same or lesser degree. This technique mirrors the traditional long division process used for numerical calculations, with the distinct difference being the use of variables and coefficients, not just numbers.

How to Do Polynomial Long Division?

Polynomial long division can be performed using the following steps:

  • Arrange the Polynomial: Write the dividend and the divisor in descending order. This means that the highest power of the variable is written first and then the lower powers are in descending order.
  • Divide the First Terms: Divide the first term (the highest degree term) of the dividend by the first term of the divisor. Write the result above the line as the first term of the quotient.
  • Multiply and Subtract: Multiply the entire divisor by the first term of the quotient. Write the result under the dividend. Subtract this from the original dividend to get a new polynomial.
  • Repeat the Process: Consider the new polynomial as the new dividend. Again, divide this new dividend's first term by the divisor's first term. Write this result as the next term of the quotient. Multiply the divisor by the new term of the quotient, write under the new dividend, and subtract.
  • Keep Going: Continue the process until the degree of the remainder (new dividend) is less than that of the divisor.
  • Get the Result: The polynomial you obtain above the line is the quotient, and the final remainder is what's left after the last subtraction step. If there's no remainder, the divisor evenly divides the original dividend.

Let's examine an example.

Suppose we have the following division problem: $$$\frac{2x^3-2x^2+3x-3}{x-1}$$$.

The process of long division would proceed as follows:

  1. Divide the highest degree term in the dividend $$$\left(2x^3\right)$$$ by the highest degree term in the divisor $$$\left(x\right)$$$. This gives us the first term of the quotient, namely, $$$\frac{2x^3}{x}=2x^2$$$.
  2. Multiply the divisor $$$x-1$$$ by the first term of the quotient $$$\left(2x^2\right)$$$ and subtract the result from the dividend. This gives us a new dividend $$$2x^3-2x^2+3x-3-2x^2(x-1)=2x^3-2x^2+3x-3-2x^3+2x^2=3x-3$$$.
  3. Repeat the process with the new dividend, dividing the highest degree term $$$\left(3x\right)$$$ by the highest degree term in the divisor $$$\left(x\right)$$$, which gives us $$$\frac{3x}{x}=3$$$. Multiply the divisor by $$$3$$$ and subtract from the new dividend, which gives us a remainder of $$$3x-3-3(x-1)=3x-3-3x+3=0$$$.

So the result of the division is $$$2x^2+3$$$.

Why Choose Our Polynomial Long Division Calculator?

  • User-Friendly Interface

    The calculator has a simple, easy-to-navigate interface that enables users of all levels to input their polynomials and receive quick solutions effortlessly.

  • Step-by-Step Guidance

    Our calculator doesn't just provide the final answer. It also outlines the step-by-step process, which can benefit those learning the concept or those who want to understand the process better.

  • Accuracy

    The calculator performs the division with high precision, eliminating the risks of human errors that can occur during manual computations.

  • Time-Efficiency

    Long division with polynomials can be a lengthy process. Our calculator provides instant results, saving valuable time and effort.


What is the formula for polynomial division?

While there isn't a specific formula for polynomial division, there is a method that can be called "divide, multiply, subtract, bring down, and repeat."

What are the two methods to divide polynomials?

There are two primary methods for dividing polynomials: long division and synthetic division. Polynomial long division is similar to the long division of numbers and can be used in all scenarios. Synthetic division is a shortcut method that works only when dividing by a linear factor $$$x - a$$$.

What should I do if I encounter an error using the calculator?

If you encounter an error, ensure you have correctly input the polynomials. If the problem persists, feel free to contact our support team.

Does the Polynomial Long Division Calculator show all the steps?

Our calculator provides the final answer and shows a detailed, step-by-step solution. This feature makes it a perfect tool for learning and understanding the polynomial long division process.