Factorise any polynomial, with every step shown

Type a polynomial in $x$, such as x^3 - 6x^2 + 11x - 6. Try to find one factor yourself before you open the working.

How to factorise a cubic by hand

1. Find a root. Try the factors of the constant term: $\pm 1,\pm 2,\pm 3,\pm 6$ for $x^3-6x^2+11x-6$. Here $p(1)=1-6+11-6=0$.
2. Use the factor theorem. $p(1)=0$, so $(x-1)$ is a factor.
3. Divide. $x^3-6x^2+11x-6=(x-1)(x^2-5x+6)$.
4. Factorise the quadratic. $x^2-5x+6=(x-2)(x-3)$.

Practise with real exam questions

• O Level 4037 factor and remainder theorem: unknown coefficients, then factorise and solve.