We perform a synthetic division

#color(white)(aaaa)##-2##color(white)(aaaa)##|##color(white)(aaaa)##2##color(white)(aaaa)##-2##color(white)(aaaaa)##0##color(white)(aaaaaa)##5##color(white)(aaaaaa)##0#

#color(white)(aaaaaa)##color(white)(aaaaa)##|##color(white)(aaa)##color(white)(aaaaaa)##-4##color(white)(aaaa)##12##color(white)(aaa)##-24##color(white)(aaaaaa)##38#

#color(white)(aaaaaaaaaa)#------------------------------------------------------------

#color(white)(aaaa)##color(white)(aaaaaa)##color(white)(aaaaaa)##2##color(white)(aaaaa)##-6##color(white)(aaaa)##12##color(white)(aaa)##-19##color(white)(aaaaaa)##color(red)(38)#

The remainder is #=38#

The quotient is #=2x^3-6x^2+12x-19#

Verification

Using the remainder theorem

#f(-2)=32+16-10=38#