Question Practice

If $x, y, z$ are distinct real numbers, then $$ \begin{vmatrix} x & x^{2} & 2 + x^{3} \\ y & y^{2} & 2 + y^{3} \\ z & z^{2} & 2 + z^{3} \end{vmatrix} = 0 $$ Then find $xyz$.