Factorising a Polynomial

Oct 2011
16
7
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
1,254
389
Belgium
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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