Factorise Expression Calculator

Work out factorise expression instantly with clear inputs, formula shown and shareable results.

About Factorise Expression Calculator

Factorising starts by extracting the highest common factor of all the coefficients, then splits what remains into linear brackets using its roots when the discriminant is non-negative.

Formula

Factorising

ax² + bx + c = g·A(x − r₁)(x − r₂) where g = gcd(a, b, c)

Worked example

With the default values below, Factorise Expression Calculator returns Factorised form of 3(2(x + 1)(x + 1.5)). Change any input above and every figure here is recalculated in your browser.

Inputs used

Coefficient of x²: 6
Coefficient of x: 15
Constant term: 9

Results

Factorised form: 3(2(x + 1)(x + 1.5))
Highest common factor extracted: 3
After removing the common factor: 2x^2 + 5x + 3
Original expression: 6x^2 + 15x + 9

Step by step

1Values used
2Factorising
3Factorised form= 3(2(x + 1)(x + 1.5))
4Highest common factor extracted= 3
5After removing the common factor= 2x^2 + 5x + 3
6Original expression= 6x^2 + 15x + 9

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 whole numbers, 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 6x² + 15x + 9.

The common factor 3 gives 3(2x² + 5x + 3), and the roots −1 and −1.5 give 3·2(x + 1)(x + 1.5) = 3(2x + 3)(x + 1).

What if the discriminant is negative?

Only the common factor can be taken out; the quadratic part is irreducible over the real numbers.