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Quick answer: enter a, b and c for ax² + bx + c above — e.g. x² + 5x + 6 factors to (x + 2)(x + 3), with roots shown.
Factoring calculator
Short answer: a factoring calculator rewrites ax² + bx + c as a product of linear factors. Enter coefficients above — roots and discriminant included.
How to factor a quadratic
Short answer: find two numbers that multiply to a·c and add to b, then split the middle term. The calculator does this instantly and shows the roots.
Frequently asked questions
How do you factor x² + 5x + 6?
(x + 2)(x + 3) — because 2 × 3 = 6 and 2 + 3 = 5. Tap the preset above to see it factored with roots.
What if the quadratic can't be factored?
If the discriminant (b² − 4ac) is negative, there are no real factors — the calculator tells you so instead of failing silently.
What is the discriminant?
b² − 4ac. Positive: two real roots. Zero: one double root. Negative: no real roots. The calculator shows it for every input.
Can it factor quadratics where a ≠ 1?
Yes — enter any a, b, c, e.g. 2x² + 7x + 3 factors to (2x + 1)(x + 3). Try the preset above.
What is factoring used for?
Solving quadratic equations, simplifying rational expressions, and finding x-intercepts of parabolas.
Is this factoring calculator free?
Yes — unlimited calculations, free forever. No account, no limits. Everything runs in your browser.