Let's perform the synthetic division

#color(white)(aaaa)##2##color(white)(aaaaa)##|##color(white)(aaaa)##2##color(white)(aaaaaa)##3##color(white)(aaaaaa)##-9##color(white)(aaaa)##-10#

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

#color(white)(aaaa)##color(white)(aaaaaaa)##|##color(white)(aaaa)##color(white)(aaaaaa)##4##color(white)(aaaaaaa)##14##color(white)(aaaaa)##10#

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

#color(white)(aaaa)##color(white)(aaaaaaa)##|##color(white)(aaaa)##2##color(white)(aaaaa)##7##color(white)(aaaaaaaa)##5##color(white)(aaaaaa)##color(red)(0)#

#(2s^3+3s^2-9s-10)/(s-2)=(2s^2+7s+5)#

The remainder is #=0# and the quotient is #=2s^2+7s+5#