About this factorization calculator
This factorization calculator focuses on two of the most common patterns in introductory algebra: quadratic trinomials and differences of squares. For a quadratic trinomial in the form ax² + bx + c, it uses an AC-style method to look for two integers that multiply to ac and add to b. When such a pair exists, the expression can be factored into two binomials over the integers. For example, x² + 5x + 6 becomes (x + 2)(x + 3). If no integer pair works, the tool explains that the quadratic does not factor nicely with integers and suggests using the quadratic formula or completing the square instead.
The calculator also recognizes the classic difference of squares pattern a² − b² = (a + b)(a − b). When you enter expressions like x² − 4, 9x² − 16, or x² − y², it rewrites them as a product of two binomials. Recognizing difference of squares is a key skill in algebra because it makes some factorizations almost immediate. This tool checks for that structure and, when it finds it, displays the factored form and a short note about the pattern.
To use the calculator, type an expression such as x² + 5x + 6, 2x² − 7x + 3, or x² − 9 and click Get result. Use standard algebra notation with lowercase variables like x and y. The output shows the factored expression in monospace font so it is easy to read, along with a brief explanation of which method was used (AC method or difference of squares). It runs entirely in your browser, is mobile-friendly, and requires no account or subscription.
Factorization is used to solve quadratic equations by setting each factor equal to zero, to simplify rational expressions by canceling common factors, and to understand the structure of polynomials. This factorization calculator is designed as a quick helper for homework, teaching, or self-study. For more advanced factoring (like sums or differences of cubes, or higher-degree polynomials), use it alongside dedicated algebra tools and your course materials. Practicing with many examples will help you recognize patterns and factor expressions more confidently on your own.