Prove that `|[yz-x^2,zx-y^2,xy-z^2],[zx-y^2,xy-z^2,yz-x^2],[xy-z^2,yz-x^2,zx-y^2]|` is divisible by `(x+y+z),` and hence find the quotient.

Explanation

To prove that the determinant

\[
D = \begin{vmatrix}
yz - x^2 & zx - y^2 & xy - z^2 \\
zx - y^2 & xy - z^2 & yz - x^2 \\
xy - z^2 & yz - x^2 & zx - y^2
\end{vmatrix}
...