Factoring Quadratics Calculator

Work out factoring quadratics instantly with clear inputs, formula shown and shareable results.

About Factoring Quadratics Calculator

Every real-rooted quadratic factorises as a(x − r₁)(x − r₂) where r₁ and r₂ come from the quadratic formula. When the discriminant is negative no real factorisation exists.

Formula

Factored form

ax² + bx + c = a(x − r₁)(x − r₂), r = (−b ± √Δ) / (2a)

Worked example

With the default values below, Factoring Quadratics Calculator returns Factorised form of (x - 3)(x - 2). Change any input above and every figure here is recalculated in your browser.

Inputs used

Coefficient a: 1
Coefficient b: -5
Coefficient c: 6

Results

Factorised form: (x - 3)(x - 2)
First root: 3.00000000
Second root: 2.00000000
Discriminant: 1.000000

Step by step

1Values used
2Factored form
3Factorised form= (x - 3)(x - 2)
4First root= 3.00000000
5Second root= 2.00000000
6Discriminant= 1.000000

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Factorise x² − 5x + 6.

The roots are 3 and 2, so it factorises as (x − 3)(x − 2).

How can I factor by inspection?

Find two numbers multiplying to ac and adding to b. For x² − 5x + 6 that is −2 and −3.