Let's perform the synthetic division

#color(white)(aaaa)##-1/2##color(white)(aaaa)##|##color(white)(aa)##2##color(white)(aaaaaaa)##1##color(white)(aaaaaa)##2##color(white)(aaaaaaa)##1#

#color(white)(aaaaaaaaaaaa)##------------#

#color(white)(aaaa)##color(white)(aaaaaaa)##|##color(white)(aaaa)##color(white)(aaaaa)##-1##color(white)(aaaaaa)##0##color(white)(aaaaa)##-1#

#color(white)(aaaaaaaaaaaa)##------------#

#color(white)(aaaa)##color(white)(aaaaaaa)##|##color(white)(aaa)##2##color(white)(aaaaaaa)##0##color(white)(aaaaaa)##2##color(white)(aaaaaa)##color(red)(0)#

The remainder is #color(red)(0)# and the quotient is #=2x^2+2#

Therefore,

#(2x^3+x^2+2x+1)=(2x^2+2)(x+1/2)#