Hi all,

Looking for some help to find if there is a "proper" way for doing this which I'm sure there is.

This is the equation.

$\displaystyle x^3 - 3x + 5 $

I'm doing lots of things to it like finding turning points etc etc, but I need to sketch it and show important points.

To do this, I need to find the x-intercept.

I really just don't know how to factorize this and get the correct answer. I know (via plugging into graphing calculator) that there is only one x intercept, and it's -2.27902. However I wish to do this 'properly' and learn how to find the factor on my own.

Factorizing doesn't seem to help, because the usual solution I would do is this.

$\displaystyle x^3 - 3x = -5 $

$\displaystyle x^2 (x - 3) = -5 $

$\displaystyle x = +/- \sqrt{-5}$ (impossible for my purposes) or $\displaystyle x = -2 $

Any help as to the proper way to do this without trial and error would be appreciated.

Cheers.