Given A=\[\begin{vmatrix}3 & 3x &3x^2+2 \\3x &3x^2+2 &3x^3+6x \\3x^2+2 &3x^3+6x &3x^4+12x^2+2 \\ \end{vmatrix}\]
using \[ C_3 \to C_3-xC_2\] \[ C_2\to C_2-xC_1\]
=\[\begin{vmatrix}3 & 0 &2 \\3x &2 &4x \\3x^2+2 &4x &3x^4+6x^2+2 \\ \end{vmatrix}\]
\[ R_3\to R_3-xR_2\] \[ R_2\to R_2-xR_1\]
=\[\begin{vmatrix}3 & 0 &2 \\0 &2 &2x \\2 &2x &2x^2+2 \\ \end{vmatrix}\]
=\[ 3(4x^2+4-4x^2)+2(-4)=4\]
