Factoring Calculator

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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