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)