Quadratic Factoring Calculator

How the quadratic factoring calculator works

Factoring a quadratic exposes the x-values that make the polynomial zero and turns multiplication into a compact description of its shape. This calculator first evaluates the discriminant, then applies the quadratic formula for both real roots. Those roots become linear factors, while a leading coefficient other than one is kept in front so the expanded expression still matches the original polynomial.

With the defaults a equals 1, b equals minus 5, and c equals 6, the discriminant is 1. The two roots are 2 and 3, so the calculator writes the verified factorization as x minus 2 times x minus 3. Expanding those factors returns x squared minus 5x plus 6, confirming that no coefficient was lost.

Reading quadratic factoring calculator results privately

A negative discriminant has complex roots, so the polynomial cannot be written as two real linear factors; the result says so explicitly. Irrational roots are displayed numerically rather than forced into an inaccurate integer form. The factorization is based on floating-point arithmetic, making it useful for algebra checks but not a symbolic proof system for expressions with parameters. This quadratic factoring calculator calculation runs entirely in your browser, so the numbers you enter never leave your device.