real analysis - Showing a continuous functions on a compact subset of $mathbb{R}^3$ can be uniformly approximated by polynomials

$\displaystyle X= \left \{\frac{x^2}{2} + \frac{y^2}{3} + \frac{z^2}{6} \leq 1 \right \}$ is a compact set

If $f(x,y,z)$ is continuous on $X$, then for any $\epsilon \gt 0$, there exists a polynomial $p(x,y,z)$ such that
$|f - p|\lt \epsilon$ on $X$.

I need to prove this and I have no idea how.