Factorize $$m^4+2m^3-m^2-2m-8$$
First I plugged numbers like $m=-3,-2,-1,0,1,2,3$ in the expression and neither of them is a root so I can't use rational roots theorem here to find a factor. I've also tried writing it as $$m^4+2m^3-m^2-2m-8=(m^2+am+b)(m^2+cm+d)$$ And expanding it gives,
$$ \begin{cases} {a+c=2} \\ {b+d+ac=-1} \\ {ad+bc=-2} \\ {bd=-8} \end{cases} $$ Then I used $a=2-c$ and changed it to three equations but still don't know how to solve it.