I need to calculate the following determinant by using the properties of determinants.
$$\begin{vmatrix} x & 1 & x^2 + 4x - 2\\ -1 & x & x^2 - 4\\ 2 & -2 & x^2 - 2x + 4 \end{vmatrix}$$
I know that the result must be $(x^3 + x + 4)(x - 2)$, but I haven't figured out how to get it yet.
Thank you in advance!