Factorising a Polynomial

Oct 2011
Hello there,

I've been asked to factorise the following expression:
\(\displaystyle x^3 - x^2 - 4x + 2\)

From what I can tell, using the factor theorem (if f(a) = 0, then (x - a) is a factor of f(x)) and factors of 2 as input to the function, it can't be factorised. Am I right, can it not be factorised? When I'm asked a question like this, should I simply say "cannot be factorised"?

I'm not asking for answers, because this is for an assignment and I don't want to cheat, I'd just like to know whether I've come to the right conclusion or not.
Jul 2011
You can't find an \(\displaystyle a\) by inspection wherefore \(\displaystyle f(a)=0\), so to solve this equation you need a numerical method. So I would say it can be factorised exactly.
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