Polynomial Long Division Calculator

- May 14, 2025

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This calculator performs polynomial long division, dividing one polynomial by another. Enter the dividend (numerator) and divisor (denominator) polynomials to find the quotient and remainder.

Polynomial Input

Dividend P(x):

Divisor D(x):

Polynomial Builder

Build Polynomial For:

Coefficient:

Power of x:

Display Options

Decimal Places:

Show division steps

About Polynomial Long Division

Polynomial long division is a method for dividing one polynomial by another, resulting in a quotient polynomial and a remainder polynomial.

Division Formula:

P(x) = D(x) × Q(x) + R(x)

Where:

P(x) is the dividend (numerator)
D(x) is the divisor (denominator)
Q(x) is the quotient
R(x) is the remainder

The degree of R(x) is always less than the degree of D(x).

Applications:

Finding Roots: Helps in finding roots of polynomials using the Remainder Theorem
Partial Fraction Decomposition: Essential for integrating rational functions
Polynomial Factorization: Assists in factoring polynomials by testing possible factors
Algebraic Simplification: Simplifies complex rational expressions

Polynomial Division Formula:
\( P(x) = D(x) \times Q(x) + R(x) \)

What Is the Polynomial Long Division Calculator?

The Polynomial Long Division Calculator is an online tool that helps you divide one polynomial by another. It provides a step-by-step breakdown of the division process, displaying the quotient and the remainder clearly. This calculator makes a traditionally manual and time-consuming Math task much easier to understand and complete.

Why Use This Calculator?

Polynomial long division is a core technique in algebra used in everything from solving equations to simplifying expressions. This calculator automates the process, providing quick, accurate results and even showing the complete division steps for better learning.

Step-by-step results: Watch how each part of the division is calculated.
Remainder and quotient: See the full solution instantly.
Input flexibility: Type your polynomials or build them term-by-term.
Visual clarity: Division is displayed in an easy-to-follow format.

How to Use the Calculator

Follow these simple steps to perform a polynomial long division:

Enter the dividend \( P(x) \) in the first field (e.g., x^3 - 2x^2 + 3x - 4).
Enter the divisor \( D(x) \) in the second field (e.g., x - 2).
Use the “Polynomial Builder” if you prefer to add each term individually with its coefficient and exponent.
Adjust the number of decimal places for rounding, if needed.
Check the “Show division steps” option to view the full breakdown.
Click Calculate to see the result.
Click Reset to clear the form and start over.

Who Can Benefit From This Tool?

This calculator is useful for anyone learning or working with algebra, from students to professionals. It’s especially helpful when you're working on related topics like:

Factoring polynomials and finding roots using tools like the Remainder Theorem Calculator.
Breaking down rational expressions for partial fraction decomposition.
Preparing for Calculus, where simplifying polynomial expressions is essential.
Using division as a stepping stone to methods like synthetic division or solving quadratic equations.

Frequently Asked Questions (FAQ)

What is polynomial long division used for?

It’s used to divide one polynomial by another. The result gives a quotient and a remainder, which helps in simplifying expressions and solving equations.

What does the formula mean?

The formula \( P(x) = D(x) \times Q(x) + R(x) \) shows that dividing polynomial \( P(x) \) by \( D(x) \) gives a quotient \( Q(x) \) and a remainder \( R(x) \).

Can this calculator help with Other math tasks?

Yes. If you're also working with percentage or error calculations, check out related tools like the Percent Error Calculator to calculate percent error or Matrix Calculator for matrix operations. You can also explore tools for scientific functions, fractions, and logarithmic equations.

Does the calculator show how the result is obtained?

Absolutely. You can toggle the option to see all the long division steps, making it a great learning companion, not just a solution tool.

How This Calculator Helps

The Polynomial Long Division Calculator simplifies a critical part of algebra. It reduces time spent on manual calculation, improves understanding of division steps, and boosts confidence in solving polynomial problems. Whether you're brushing up on algebra or solving real-world equations, this tool gives clear answers and teaches you along the way.