Algebra
# Advanced Factorization

If $P(n)=\frac{n^3+n^2-2n}{n^2-4}+\frac{n+1}{2+n-n^2}$, what is the value of $\lfloor P(409) \rfloor + \lfloor P(423) \rfloor$?

**Details and assumptions**

The function $\lfloor x \rfloor: \mathbb{R} \rightarrow \mathbb{Z}$ refers to the greatest integer smaller than or equal to $x$. For example, $\lfloor 2.3 \rfloor = 2$ and $\lfloor -5 \rfloor = -5$.

$x, y$ and $z$ are complex numbers such that

$\begin{cases} x + y + z & = 46 \\ (x-y)^2 + (y-z)^2 + (z-x) ^ 2 & = xyz.\\ \end{cases}$

What is the value of $\frac{ x^3 + y^3 + z^3} { xyz}$?