Factoring is algebra's version of reverse engineering — instead of multiplying out, you're asking what multiplied together made this. The quadratic x² − 5x + 6 factors into (x − 2)(x − 3), and suddenly the equation x² − 5x + 6 = 0 surrenders its solutions: x = 2 or x = 3, because a product is zero exactly when one of its factors is zero. That zero-product property is why factoring matters — it converts a hard equation into two easy ones, and it shows up on every Algebra I final and SAT math section.

The discriminant b² − 4ac is your scouting report before you factor: positive means two real roots worth hunting, zero means one repeated root, negative means the quadratic never touches the x-axis and you'll need complex numbers. Vieta's formulas give you a second opinion — the roots must sum to −b/a and multiply to c/a, so for x² − 5x + 6 the roots 2 and 3 check out (5 and 6). This calculator runs all of it: enter a, b, c and read the discriminant, both roots, and the Vieta sum and product. When a quadratic won't factor over integers (try x² + x + 1), the discriminant tells you immediately instead of letting you hunt ghosts.

With the pre-filled defaults — a (x² coefficient) 1, b (x coefficient) -5, c (constant) 6 — the Factoring Calculator returns Discriminant b² − 4ac 1.0000, Root 1 (x₁) 3.000000, Root 2 (x₂) 2.000000, Sum of Roots (−b/a) 5.000000, Product of Roots (c/a) 6.000000. Change any input and those results update instantly, so you can see exactly how each number you enter moves the answer.