How to use this quadratic factoring calculator
Find real roots and a real linear factorization of ax² + bx + c. Start with the labeled example values, then replace them with the figures for your problem. Keep units consistent. Results update as you type. If an entry is invalid, the result is cleared and the page explains what needs attention, rather than showing a stale answer.
Formula and calculation method
For ax² + bx + c, the discriminant is b² − 4ac. A positive discriminant produces two real roots, zero gives a repeated root, and a negative value gives no real roots. For roots r1 and r2, the real factorization is a × (x − r1) × (x − r2).
Worked example
For x² − 5x + 6, the discriminant is 25 − 24 = 1. The roots are 2 and 3, so the expression factors as (x − 2)(x − 3). Expanding confirms x² − 5x + 6. Check both the leading coefficient and signs when copying a polynomial into the fields.
Assumptions and limitations
This tool handles quadratics, not arbitrary symbolic expressions or prime factorization. Irrational roots are shown numerically, so a displayed factorization may be approximate. A negative discriminant is reported without complex factoring. Coefficient a cannot be zero; linear equations require a different calculation.
Check and keep your result
Check the example by hand before applying the result to your own figures. Download the result to retain the inputs with the output, or use Print for a paper copy. Calculations run locally in your browser and entries are not sent to our server. The website’s advertising services operate separately; see our privacy policy.
Created and calculation-tested by Velour Trends · Updated 8 November 2026. No independent professional review is claimed. Report a calculation issue.