Set up the divisor and dividend as if doing normal long division:
#color(white)("xxxxxxxx")ul(color(white)("xx")color(white)(x^3)color(white)("xxxxxxx")color(white)(-1/2x)color(white)("x")color(white)(+7/2)color(white)("xxxxxxxxxxxx")#
#2x^2+1color(white)("x"))color(white)("x")2x^5color(white)("x")+0x^4color(white)("x")+0x^3color(white)("x")+7x^2color(white)("x")+5xcolor(white)("x")+1#
Divide the first term of the divisor into the first term of the dividend and write the (partial) quotient above the line:
#color(white)("xxxxxxxx")ul(color(white)("xx")color(red)(x^3)color(white)("xxxxxxx")color(white)(-1/2x)color(white)("x")color(white)(+7/2)color(white)("xxxxxxxxxxxx")#
#color(blue)(2x^2)+1color(white)("x"))color(white)("x")color(blue)(2x^5)color(white)("x")+0x^4color(white)("x")+0x^3color(white)("x")+7x^2color(white)("x")+5xcolor(white)("x")+1#
Multiply the entire divisor by the quotient term just calculated and subtract their product from the dividend to get a reduced dividend.
#color(white)("xxxxxxxx")ul(color(white)("xx")color(blue)(x^3)color(white)("xxxxxxx")color(white)(-1/2x)color(white)("x")color(white)(+7/2)color(white)("xxxxxxxxxxxx")#
#color(blue)(2x^2+1)color(white)("x"))color(white)("x")2x^5color(white)("x")+0x^4color(white)("x")+0x^3color(white)("x")+7x^2color(white)("x")+5xcolor(white)("x")+1#
#color(white)("xxxxxxxxx")ul(color(red)(2x^5color(white)("xxxxxxxx")+1x^3color(white)("xxxxxxxxxxxxxxxx"))#
#color(white)("xxxxxxxxxxxxxxxxxxxx")color(red)(-1x^3color(white)("x")+7x^2color(white)("x")+5xcolor(white)("x")+1)#
Repeat this process until no further divisions are possible.
#color(white)("xxxxxxxx")ul(color(white)("xx")color(red)(x^3color(white)("xxxxxxx")-1/2xcolor(white)("x")+7/2color(white)("xxxxxxxxxxxx"))#
#2x^2+1color(white)("x"))color(white)("x")2x^5color(white)("x")+0x^4color(white)("x")+0x^3color(white)("x")+7x^2color(white)("x")+5xcolor(white)("x")+1#
#color(white)("xxxxxxxxx")ul(2x^5color(white)("xxxxxxxx")+1x^3color(white)("xxxxxxxxxxxxxxxx")#
#color(white)("xxxxxxxxxxxxxxxxxxxx")-1x^3color(white)("x")+7x^2color(white)("x")+5xcolor(white)("x")+1#
#color(white)("xxxxxxxxxxxxxxxxxxxx")ul(-1x^3color(white)("xxxxxxx")-1/2xcolor(white)("xxxx")#
#color(white)("xxxxxxxxxxxxxxxxxxxxxxxxxxxx")7x^2+11/2xcolor(white)("x")+1#
#color(white)("xxxxxxxxxxxxxxxxxxxxxxxxxxxx")ul(7x^2color(white)("xxxxxxx")+7/2)#
#color(white)("xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx")color(red)(11/2xcolor(white)("x")-5/2)#
