How can I factor a cubic function with a given x-intercept?

[Calcuconfused]

Alright, so I need a little brush up on my pre calc apparently! I need to determine the x-intercepts of the following function.

y=x^3 + 2

I know I need to factor it... I'm just not completely sure how! Thanks!

 

[Nessdude14]

There's no need to factor. The x-intercepts are when y=0, so you just need to solve the equation:

$0=x^3+2$

 

[Mentallic]

Calcuconfused, If you move the 2 onto the other side of $0=x^3+2$ and then take the cube root of both sides, you'll end up with $$x=-\sqrt[3]{2}$$ so if you were to try and factor it (in case you need to find the factors for another purpose, such as to show what all 3 roots are) you're going to have an ugly thing to factor.

But regardless, if you need to factor it, you'll end up with a linear factor and a quadratic factor, and since we've already shown one of the roots, the end result will be of the form

$$\left(x+\sqrt[3]{2}\right)\left(x^2+ax+\sqrt[3]{4}\right)$$

For some yet to be found constant value a.