Factoring Calculator
Factor polynomials with step-by-step solutions. Supports GCF, difference of squares, trinomials, grouping, and sum/difference of cubes.
Formula:ax² + bx + c = a(x - r₁)(x - r₂)
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f(x)
Factoring Practice Problems
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Practice with 5 problems to test your understanding.
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What is Factoring?
Factoring is the process of breaking down a polynomial into a product of simpler polynomials. It is the reverse of expanding (multiplying). Factoring is essential for solving equations, simplifying expressions, and understanding polynomial behavior.
Factoring converts a polynomial into a product of simpler factors. Use our free calculator to factor any polynomial instantly with step-by-step solutions. Simply enter expressions like x^2 - 9, x^2 + 5x + 6, or 2x^2 - 8 and get the factored form with detailed explanations.
Key Factoring Rules
- •GCF Factoring: Always check for a greatest common factor first
- •Difference of Squares: a² - b² = (a + b)(a - b)
- •Perfect Square Trinomial: a² ± 2ab + b² = (a ± b)²
- •Trinomial: x² + bx + c = (x + p)(x + q) where pq = c and p + q = b
- •Sum of Cubes: a³ + b³ = (a + b)(a² - ab + b²)
- •Difference of Cubes: a³ - b³ = (a - b)(a² + ab + b²)
- •Some polynomials are prime (cannot be factored over integers)
- •Always verify by multiplying factors back together
Frequently Asked Questions
How do I factor x² - 9?
This is a difference of squares: x² - 9 = x² - 3² = (x + 3)(x - 3). The formula a² - b² = (a + b)(a - b) applies whenever you have a perfect square minus another perfect square.
How do I factor x² + 5x + 6?
This is a trinomial. Find two numbers that multiply to 6 (the constant) and add to 5 (the coefficient of x). Those numbers are 2 and 3, so x² + 5x + 6 = (x + 2)(x + 3).
Why can't I factor x² + 1?
x² + 1 is prime over the real numbers because there are no two real numbers that multiply to give 1 and add to give 0. It can only be factored using complex numbers: (x + i)(x - i).
What is the AC method?
The AC method is used for trinomials ax² + bx + c where a ≠ 1. Multiply a and c, find two numbers that multiply to ac and add to b, then use grouping to factor.
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How this works
Formulas follow standard definitions from the NIST Digital Library of Mathematical Functions and classical textbook derivations. Calculations run entirely in your browser. Where a closed-form solution exists, it is used; where an iterative or numerical method is required, the implementation is named on the page.
Sources
- [1]NIST Digital Library of Mathematical FunctionsAcademicdlmf.nist.govAccessed Apr 21, 2026
Joseph OrdunaFounder & Software Engineer
Full-stack software engineer specializing in embedded systems, web architecture, and AI/ML. Founder of Practical Web Tools. Built the gesture-controlled drone IP acquired by KD Interactive (Aura Drone, sold on Amazon).