Determine all values of x for which f is not defined.
f(x) = (2x^3 + 5x^2 -22x + 15) / (2x^3 + 15x^2 - 34x + 24)
Is there a typo here? I'm not getting a nice answer here...
You need to find where the denominator is zero, so the problem becomes how do you find the zeros of
$\displaystyle 2x^3 + 15x^2 - 34x + 24$
Well, all rational zeros of this polynomial have the form
$\displaystyle \frac{\text{factors of }24}{\text{factors of }2}$
So your list of possible rational zeros is
$\displaystyle \pm(\frac{1}{2}, 1, 2, 3, 4, 6, 8, 12, 24)$
Since none of these work you need to resort to something like Cardano's method (very ugly) or numerical approximation. I get that there is one real zero around -9.44.
-Dan