Algebra

Polynomial factoriser

Rational roots and factors up to degree 6, with steps.

For checking your work after you’ve tried it yourself.

Step 1:
Type a polynomial

In x, up to degree 6, like x^3 - 6x^2 + 11x - 6.

Step 2:
Check how it's read

The preview shows the polynomial as the tool understood it.

Step 3:
Press Factorise

Then compare and open Do it by hand.
What it does.
Factorises a polynomial in xx with rational coefficients, up to degree 6. It finds every rational root with the rational root test, divides each one out, and handles the quadratic that's left, giving roots with square roots when they aren't rational.
When it helps.
Checking a factorisation, or the roots you found by hand.
What it won’t do.
It may not split a leftover of degree 3 or more that has no rational roots, and it says so when that happens.
Example.
x3−6x2+11x−6=(x−1)(x−2)(x−3)x^3 - 6x^2 + 11x - 6 = (x-1)(x-2)(x-3).

Use ^ for powers: x^3 - 6x^2 + 11x - 6. Fractions like x^2/2 are fine.

Try