Factoring Trinomials Calculator

Factor ax² + bx + c by finding its roots.

Root 1 3
Root 2 2
Discriminant 1

Formula: Factors as a(x − r₁)(x − r₂)

Step-by-step with your numbers:
1. Values used:
2. a = 1
3. b = -5
4. c = 6
5.
6. Root 1 = 3
7. Root 2 = 2
8. Discriminant = 1
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Factoring a trinomial means writing it as a product of two binomials using its roots.

The math behind it

Find the roots r₁ and r₂ with the quadratic formula; then ax² + bx + c = a(x − r₁)(x − r₂). Real factors exist only when the discriminant b² − 4ac ≥ 0.

Worked example

x² − 5x + 6 → roots 2 and 3 → (x − 2)(x − 3).

FAQ

What if the discriminant is negative?

The trinomial has no real factors; it factors only over the complex numbers.