Let's perform the synthetic division

Let #f(x)=3x^4-2x^3+5x^2-4x-2#

Let's perform the synthetic division

#color(white)(aaaa)##-1##color(white)(aaaaa)##|##color(white)(aaaa)##3##color(white)(aaaaaa)##-2##color(white)(aaaaaa)##5##color(white)(aaaaa)##-4##color(white)(aaaaa)##-2#

#color(white)(aaaaaaaaaaaa)#*_**_**_**_**_*____

#color(white)(aaaa)##color(white)(aaaaaaa)##|##color(white)(aaaa)##color(white)(aaaaaaa)##-3##color(white)(aaaaaaa)##5##color(white)(aaaaa)##-10##color(white)(aaaa)##14#

#color(white)(aaaaaaaaaaaa)#*_**_**_**_**_*___

#color(white)(aaaa)##color(white)(aaaaaaa)##|##color(white)(aaaa)##3##color(white)(aaaaaa)##-5##color(white)(aaaaaaa)##10##color(white)(aaaa)##-14##color(white)(aaaaa)##color(red)(12)#

#f(x)=(3x^3-5x^2+10x-14)+12/(x+1)#

The remainder is #=-2#