Factoring Quadratics Calculator
Solve ax² + bx + c = 0 with the full quadratic formula worked out step by step: exact roots like (3 ± √5)/2 or −1 ± 2i, the discriminant, the vertex and the factored form.
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Result
About this tool
This page opens the quadratic equation solver with the factored-form card put first: enter a, b and c and, whenever the roots are rational, the trinomial is rewritten as a product of integer factors. The default example x² − 3x + 2 factors as (x − 1)(x − 2) because its roots are x = 1 and x = 2.
The factoring comes straight from the quadratic formula: the solver computes the discriminant, checks that it is a perfect square, finds the roots as reduced fractions p/q, and assembles factors of the form (qx − p) — so 6x² − 5x + 1 with roots 1/2 and 1/3 becomes (2x − 1)(3x − 1), and a double root gives a perfect square like (x − 2)².
When the discriminant is not a perfect square the tool says so honestly — the trinomial does not factor over the rational numbers — and shows the exact radical roots instead, which is precisely the boundary between 'factor it' and 'use the formula' exercises. Either way the full step list documents the decision.
Example. The equation x² − 5x + 6 = 0 returns roots 2 and 3 and discriminant 25.
Limit. The leading coefficient cannot be zero, and each coefficient may contain at most 9 digits.