\[a^{3}x^{2} - ax - 4a^{3} - 2a =\]
\[= a^{3}\left( x^{2} - 4 \right) - a(x + 2) =\]
\[= a^{3}(x - 2)(x + 2) - a(x + 2) =\]
\[= a(x + 2)\left( a^{2}x - 2a^{2} - 1 \right)\]