Factoring Polynomials Calculator

Factor polynomials step by step

The calculator will try to factor any polynomial (binomial, trinomial, quadratic, etc.), with steps shown. The following methods are used: factoring monomials (common factor), factoring quadratics, grouping and regrouping, square of sum/difference, cube of sum/difference, difference of squares, sum/difference of cubes, the rational zeros theorem. The calculator accepts both univariate and multivariate polynomials.

Enter a polynomial:

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.

Handling polynomials is made easier with our Factoring Polynomials Calculator. Whether you're tackling a challenging polynomial or merely refining your algebra knowledge, this tool is designed to ease the task.

How to Use Our Factoring Polynomials Calculator?

  • Input

    Begin by entering your polynomial into the designated field. Ensure that the coefficients and terms are correctly inputted.

  • Calculation

    After inputting the polynomial, click the "Calculate" button.

  • Result

    The calculator will display the factored form of the polynomial. If the polynomial can't be factored, the calculator will notify you.

What Is Factoring?

Factoring, in mathematics, refers to decomposing a mathematical expression or number into a product of other numbers or expressions. When you factor an expression, you find two or more quantities that, when multiplied together, give the original expression.

For instance, consider the number $$$10$$$. It can be factored as $$$2\cdot5$$$. Here, $$$2$$$ and $$$5$$$ are the factors of $$$10$$$.

Why Is Factoring Important?

Understanding the factors of a polynomial is crucial in solving polynomial equations. It's akin to breaking down a problem into smaller, more manageable pieces. With a grasp of the essential factoring methods and techniques, you can solve a wide range of mathematical problems more effectively.

What Is Factoring Polynomials?

Factoring polynomials is a process in algebra where a polynomial is expressed as the product of two or more polynomial factors. It's akin to breaking down a number into its prime factors. By factoring, we are looking for polynomial expressions that, when multiplied together, will produce the original polynomial.

For example, the polynomial $$$x^2-9$$$ can be factored as $$$(x+3)(x-3)$$$. Another example is $$$x^2+5x+6$$$, whose factors are $$$x + 2$$$ and $$$x + 3$$$.

Factoring polynomials is a foundational technique in algebra, serving various purposes:

  • Simplifying complex expressions.
  • Solving polynomial equations.
  • Graphing polynomial functions, since the zeros (roots) of the polynomial can be easily identified once the polynomial is factored.

Different methods are used to factor polynomials depending on their form and degree, including:

  • Factoring out the greatest common factor (GCF).
  • Grouping.
  • Using unique factorization formulas like the difference of squares or cubes.
  • Quadratic trinomials factoring, and more.

The ability to factor polynomials can greatly assist in understanding and solving more complex mathematical problems.

Why Choose Our Factoring Polynomials Calculator?

  • Accuracy Assured

    Our calculator processes even the most complex polynomials, ensuring accurate factorization every time.

  • User-Friendly Design

    With an intuitive interface, even those new to the world of algebra will find it simple to use.

  • Step-by-Step Solutions

    Beyond just answering, our tool provides detailed solutions, breaking down the factoring process for enhanced understanding.

  • Versatility

    Whether you're tackling quadratic trinomials, cubic equations, or higher-degree polynomials, our calculator is up to the task.


How do I input my polynomial?

Simply enter your polynomial in the provided input field, ensuring you include all coefficients and variables. Then, click on the "Calculate" button.

What is the Factoring Polynomials Calculator used for?

The Factoring Polynomials Calculator is designed to help users break down a polynomial into its simplest factors. This assists in understanding and solving polynomial equations more efficiently.

I'm new to polynomials. Do you provide any explanations or steps?

Yes, our calculator offers a step-by-step breakdown of the factoring process, making it easier for learners to understand the methodology behind the results.

How is factoring polynomials helpful in real-life situations?

Factoring polynomials is a fundamental skill in algebra. It's crucial for solving polynomial equations, which have applications in engineering, physics, and economics.