Question 806049
Include the power of 2 and of 1 in the dividend.


___________|______x^2_______2x___________4___
___________|_________________________________
x-2________|______x^3______0*x^2________0*x_________-6
___________|______x^3______-2x^2
___________|______________________
__________________0_________2x^2________0*x
____________________________2x^2________-4x
____________________________________________
_____________________________0___________4x________-6
_________________________________________4x________-8
________________________________________________________
____________________________________________________+2





Start with asking {{{x^3/x=x^2}}}.  The numerator is from the dividend and the denominator is from the divisor.  Put the partial quotient in the top line above the x^3 of the dividend.  The rest of this step is just like regular long division.


Continue the process for the next term of the dividend.


The result gives remainder of +2.
The resulting division is {{{highlight(x^2+2x+4+2/(x-2))}}}