Factoring Calculator

Factor a polynomial using the appropriate pattern, then check your result by expanding it.

ai math solver for factoring

See How Factoring Undoes Multiplication

Rewrite a polynomial by expressing it as a product of simpler factors. Start by looking for the greatest common factor, then consider the number of terms and the powers involved to identify the factoring pattern that applies.

A correct factorization should produce the original polynomial when the factors are multiplied together. Expanding the factors afterward is a simple way to confirm the result and catch any errors with signs.

Using the Factoring Calculator

Here is how to use factoring calculator:

Type in the Original Expression

Enter or paste the complete expression. You can also upload a clear photo or PDF and review the extracted text before solving.

 Follow the Steps Behind the Result

Each step is clearly broken down and explained, allowing you to compare the process with your own approach.

Explore Any Step You Find Unclear

Stay within the same solution to try another method, verify a restriction, or understand why a particular rule applies.

Recognizing a Difference of Squares

The difference between two perfect squares can be factored into a pair of conjugate binomials.

a² − b² = (a − b)(a + b)

A Simple Method for Factoring Expressions

A reliable approach is to work through the following steps:

Find the Greatest Common Factor

Find the greatest factor shared by every term before trying any other factoring pattern.

Factor Quadratic Trinomials

Choose terms that multiply to ac and add to b, then group them.

Recognize Common Special Products

You can recognize some special products by adding them

 Worked Example: Factor 6x² + 11x -10

ac  = 6 (-10) = -60           Find the product of leading coefficient and constant. 

15+(-4)= 11                      Find the factors of -60 that sum to 11.

6x² + 15x − 4x − 10            Break the middle terms into two terms.

3x(2x + 5) − 2(2x + 5)     Factors each set of terms.

(3x-2) (2x+5)                    Take out the common binomial factor.

                                         The complete Factorization is (3x-2) (2x+5)

Common Factoring Errors to Avoid

Here are some common factoring mistakes to watch for.

Overlooking the GCF

Factoring is incomplete when all the terms still contain common factors.

Mistaking a Sum of Squares for a Factorable Pattern

Unlike a² − b², a² + b² does not factor over the real numbers in the same way. 

Forgetting to Check by Multiplication

Expanding the factors confirms the middle term and sign choices. 

More Calculators to Try

Frequently Asked Questions About Factoring

Yes. The calculator can factor trinomials where the leading coefficient a is not 1. Enter the trinomial as written, and it will work through the factoring steps to find the factors when suitable factorization exists.

Yes. The calculator can factor higher-degree polynomials when they can be factored using supported methods. Enter the polynomial as written to see the available factors and steps.

If a polynomial is prime, it cannot be factored into lower-degree polynomial factors over the chosen number system. The calculator shows the original polynomial when no further factorization is possible.

Yes. Factoring can make questions easier to solve by rewriting an expression as a product of factors. Once the question is factored, you can use the zero-product property to find the possible solutions. Like factor & factoring you should know about Chain Rule VS Product Rule.