\(-4x^3\left(ax^2+bx+x\right)=-8x^5+12x^4-20x^3\)

\(\Rightarrow-4ax^5-4bx^4-4bx^3=-8x^5+12x^4-20x^3\)

\(\Rightarrow\left\{{}\begin{matrix}-4ax^5=-8x^5\\-4bx^4=12x^4\\-4cx^3=-20x^3\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}a=2\\b=-3\\c=5\end{matrix}\right.\)

\(x^4-2x^3+5x^2-8x-4\)

\(=x^4-2x^3+5x^2-10x+2x-4\)

\(=x^3\left(x-2\right)+5x\left(x-2\right)+2\left(x-2\right)\)

\(=\left(x-2\right)\left(x^3+5x+2\right)\)