Here ,
Dividend #:color(blue)(2x^3+2x^2+4x+4) and#
divisor #: color(red)(x^2+8x+4)#
So ,
#color(white)(..................................)color(green)(ul(2x-14color(white)(.........))larrquotient#
#color(white)(..........)color(red)((x^2+8x+4)) # #|color(blue)(2x^3+2x^2+4x+4)# ##
#color(white)()color(violet)((color(red)(x^2+8x+4))*2xtocolor(white)()ul(2x^3+16x^2+8x)##color(white)(.......)lArr"subtract"#
#color(white)(.....................................)-14x^2-4x+4#
#color(white)()color(violet)((color(red)(x^2+8x+4))(-14)tocolor(white)()ul(-14x^2-112x-56)##color(white)(.......)lArr"subtract"#
#color(white)(..........................................)color(green)(##color(white)(.........)108x+60larr"Remainder"#
Hence ,
#(color(blue)(2x^3+2x^2+4x+4))#=#(color(red)(x^2+8x+4))(2x-14)+(108x+60)#
#Quotient :q(x)=color(green)(2x-14# #"and Remainder " :r(x)=108x+60#