\[\begin{array}{l}
3{x^4} - 8{x^3} - 10{x^2} + 8x - 5\\
= (3{x^4} - 2{x^3} + {x^2}) - (6{x^3} - 4{x^2} + 2x) - (15{x^2} - 10x + 5)\\
= {x^2}(3{x^2} - 2x + 1) - 2x(3{x^2} - 2x + 1) - 5(3{x^2} - 2x + 1)\\
= (3{x^2} - 2x + 1)({x^2} - 2x - 5)
\end{array}\]