Determinant of a $3 \times 3$ matrix involving a variable 
I'm trying to find the determinant of 
  $$A=\begin{bmatrix}x& x^2 &x^3 \\x^8 & x^9 & x^4\\x^7 & x^6 & x^5 \end{bmatrix}$$

I'm using the cofactor formula, 
$det(A)=x(x^{14}-x^{10})+x^2(x^{11}-x^{13})+x^3(x^{14}-x^{16})$
$=x^{15}-x^{11}+x^{13}-x^{15}+x^{17}-x^{19}$
$=-x^{11}+x^{13}+x^{17}-x^{19}$
$=x^{10}(-x+x^3+x^7-x^9)$
Is there any other method to find this? 
I'm totally stuck on row reduction. Any help?

By Sarrus rule,
\begin{align*}
\det(A)&=x^{1+9+5}+x^{2+4+7}+x^{3+8+6}-x^{7+9+3}-x^{6+4+1}-x^{5+8+2}\\
&=x^{15}+x^{13}+x^{17}-x^{19}-x^{11}-x^{15}\\
&=x^{11}(x^2+x^6-x^8-1) \\
&=-x^{11}(x^6-1)(x^2-1)\\
&=-x^{11}(x^2+x+1)(x^2-x+1)(x-1)^2(x+1)^2.
\end{align*}
