Factor Theorem Calculator

Work out factor theorem instantly with clear inputs, formula shown and shareable results.

About Factor Theorem Calculator

The factor theorem is the remainder theorem's zero case: (x − a) divides P(x) exactly when P(a) = 0. Dividing out then reduces the degree by one, ready for further factorising.

Formula

Factor theorem

(x − a) is a factor of P(x) ⇔ P(a) = 0

Worked example

With the default values below, Factor Theorem Calculator returns Result of (x - 1) is a factor. Change any input above and every figure here is recalculated in your browser.

Inputs used

Polynomial coefficients, highest power first: 1, -6, 11, -6
Test whether (x − a) is a factor, with a =: 1

Results

Result: (x - 1) is a factor
P(a): 0.00000000
Remaining factor after division: x^2 - 5x + 6
Polynomial entered: x^3 - 6x^2 + 11x - 6

Step by step

1Values used
2Factor theorem
3Result= (x - 1) is a factor
4P(a)= 0.00000000
5Remaining factor after division= x^2 - 5x + 6
6Polynomial entered= x^3 - 6x^2 + 11x - 6

Assumptions and limits

The result is derived only from the 2 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

Is (x − 1) a factor of x³ − 6x² + 11x − 6?

P(1) = 1 − 6 + 11 − 6 = 0, so yes, and the quotient is x² − 5x + 6.

How do I find candidate values of a?

Use the rational root theorem: test factors of the constant term divided by factors of the leading coefficient.