Direct substitution
#f(-2)=-16-64-26-4=-110#
The remainder is #=-110#
We perform a synthetic division
#color(white)(aaaa)##-2##color(white)(aaaa)##|##color(white)(aaaa)##-1##color(white)(aaaa)##8##color(white)(aaaaa)##0##color(white)(aaaaaa)##13##color(white)(aaaa)##-4#
#color(white)(aaaaaa)##color(white)(aaaaa)##|##color(white)(aaa)##color(white)(aaaaaaa)##2##color(white)(aaaaa)##-20##color(white)(aaaa)##40##color(white)(aaaaa)##-106#
#color(white)(aaaaaaaaaa)#------------------------------------------------------------
#color(white)(aaaa)##color(white)(aaaaaa)##color(white)(aaaaaa)##-1##color(white)(aaa)##10##color(white)(aaaaa)##-20##color(white)(aaaaa)##53##color(white)(aaaaa)##color(red)(-110)#
The remainder is #=-110#
The quotient is #=-x^3+10x^2-20x+53#