Factoring Calculator
Factor polynomials with step-by-step solutions. Supports GCF, difference of squares, trinomials, grouping, and sum/difference of cubes.
Enter Expression
Factoring Practice Problems
Test your skills with practice problems
Practice with 5 problems to test your understanding.
Try These Examples
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?
How do I factor x² + 5x + 6?
Why can't I factor x² + 1?
What is the AC method?
Related Math Tools
Explore similar calculators