Originally Posted by

**Joker37** Use short division to factorise x^3 - 5x^2 - 2x + 24.

*I don't know how to use short division to factorise this cubic polynomial. I only know how to factorise it through long division. If anyone could show a very simple worked out solution to this it will be appreciated!*

Hi Joker37,

$\displaystyle x^3 - 5x^2 - 2x + 24.$

The first thing I would do is try to find a rational root if f(x)=0. According to the Rational Root Theorem, the possibilites are +/-1, +/-2, +/-3, +/-4, +/-6, +/-8, +/-12, +/-24.

I found that f(3)=0, so I will use synthetic division to find the depressed quadratic which should be easier to factor.

Code:

3 | 1 -5 -2 24
3 -6 -24
--------------
1 -2 -8 0

The resulting quadratic is $\displaystyle x^2-2x-8$ which can easily be factored into

$\displaystyle (x-4)(x+2)$

So

$\displaystyle x^3 - 5x^2 - 2x + 24=(x-3)(x-4)(x+2).$