# factorising cubics

• Apr 6th 2010, 04:35 AM
Tekken
factorising cubics
is there any formula or neat trick to factorise a cubic equation like

x^3 + 4x^2 -28x + 32=0?
• Apr 6th 2010, 05:01 AM
Prove It
Quote:

Originally Posted by Tekken
is there any formula or neat trick to factorise a cubic equation like

x^3 + 4x^2 -28x + 32=0?

Yes, use the factor and remainder theorems.

For any polynomial $P(x)$, if $P(a) = 0$ then $x - a$ is a factor.

The factors of $32$ are $\pm 1, \pm 2, \pm 4, \pm 8, \pm 16, \pm 32$.

So try substituting these values into the expression.
• Apr 6th 2010, 05:11 AM
HallsofIvy
That will allow you to find any factors with rational coefficients. More generally, you could use Cardano's cubic formula to find a solution, $x_0$, then divide by $x- x_0$ to reduce the problem to factoring a quadratic.