Factoring Calculator

Factoring means writing the expression as a product of simpler expressions. For example, x² + 5x + 6 factors as (x + 2)(x + 3). Factoring is the reverse of expanding (FOIL).

Quadratic expressions ax² + bx + c with integer roots, the difference of two squares like 9x² − 16, linear expressions ax + b where a and b share a common factor, and any combination once the greatest common factor is pulled out.

If the discriminant b² − 4ac is negative, the quadratic has no real roots and cannot factor over the integers or the reals. If the discriminant is positive but not a perfect square, the roots are irrational and the factoring would not be clean. In both cases the calculator says so instead of pretending.

The quadratic formula calculator returns the roots of ax² + bx + c = 0, even when the roots are irrational or complex. The factoring calculator returns the factored form when it exists as a clean product of binomials with integer coefficients.

Not directly. It supports degree-2 quadratics (and linears and constants). For higher-degree work, you usually factor by grouping, by inspection, or with synthetic division after finding a rational root.

Any expression of the form a²x² − b² with a and b positive integers matches the identity a²x² − b² = (ax − b)(ax + b). The calculator checks whether the leading coefficient and the negated constant are both perfect squares.