#color(white)(.......)color(white)(..)color(magenta)(x^3-x^2-2x+2#
#x+1|overline(x^4+0-3x^2+0+12)#
#color(white)(............)ul(x^4+x^3)#
#color(white)(...............)-x^3-3x^2#
#color(white)(................)ul(-x^3-x^2)#
#color(white)(.......................)-2x^2+0#
#color(white)(.........................)ul(-2x^2-2x)#
#color(white)(......................................)2x+12#
#color(white)(.......................................)ul(2x+2)#
#color(white)(..............................................)10#
#color(magenta)((x^4+3x^2+12) / (x+1) = x^3-x^2-2x+2# and remainder of #color(magenta)(10/(x+1)#