# Factorising Cubic Equations - Maths Help

Found 2nd Mar 2009
I have a practise C1 exam tomorrow for my AS Level Maths & I am revising at the moment & cannot work out how to factorise a cubic equation which I have from a different past paper.

I could probably get it after a while but if anyone knows a way to generally factorise cubics I would be greatful if you could explain as my notes dont seem to make sence to me.

The said equation is x ^ 3 - 3x ^ 2 - 6x + 8

I have tried getting a linear & quadratic from it but I cant seem to get it right. In the end I need 3 linear factors of it.

If anyone could explain I would be very greatful. Its a non calculator paper so shouldnt be too complex.

Thanks alot

Cheers
James
You can use synthetic division to factorise cubics: purplemath.com/mod…htm

You'll need to guess a factor, such as 1 or -2 etc. It's a factor if the remainder is 0.

I learnt this at Higher level (A level) Maths, and it is very useful.
You need to remove a factor of x from the equation to make it a quadratic, then simplify from there. Or so I think... 3 years since I've done A2 maths.
Managed it after about an hour of messing around on various sites & trial & error.

It was...

(x-1)(x^2 - 2x -8)

(x-1)(x+2)(x-4)

Need to go over them before tomorrow though haha!

Cheers for the replies!
The factor was 1. Managed to work it out synthetic division.

At least you got it sorted.
How did you get the factor mate?

May come in handy tomorrow.

Cheers
James
One way to get started is to look at the unit (the element without x). In this case its 8 - which, assuming all the factors use integers, can only be factored with 1,2 & 4 or 1,1 & 8. As there are a couple of negative elements in the equation but the '8' is positive, you know that 2 of the factors must be (x - ..) instead of (x + ..). So just from these simple deductions you've reduced the number of possibilities to only 5, which are easy to multiply out and find the correct one...:
(x - 1)(x - 2)(x + 4)
(x - 1)(x + 2)(x - 4)
(x + 1)(x- 2)(x - 4)
(x - 1)(x - 1)(x +
(x - 1)(x + 1)(x +
use the F of (x) thing. I did C1 in January (epic fail)... C2 and Mechs in june
James...;4533377

How did you get the factor mate?May come in handy tomorrow.CheersJames

The factor was just guessed. If if is non calculator, the factor will be a small number that you can do in your head. If the remainder is 0 (using synthetic division), then its a factor.
Here is a sketchy method I made in Paint:
Thanks again for the replies, been a great help & made it sound alot more simple, hopefully the exam goes alright, got a C in the last one but got back from Australia the day before & missed 3 weeks of revision & didnt know I had the test, should be better prepared this time hopefully!