Question 954308
Polynomial Division is not more difficult than Long Division for base-ten numbers.  The process can be easier to understand as you see each part of the process.  You still pay attention to place-value, and still look for numbers to subtract and count them as you form the parts of the quotient.


Either you know how or not know how to perform polynomial division.   I will use factoring through trial inspection instead.


{{{(x-2)(x+w)=x^2+2x-8}}}
{{{system(-2x+wx=2x, -2w=-8)}}}
{{{system(w-2=2,w=4)}}}


Factorization is  {{{(x-2)(x+4)}}}.


You are looking for the rational equation  {{{highlight((x^2+2x-8)/(x-2)=x+4)}}}.



REMINDED:
The question is a writing assignment.  The tutors cannot or at least should not do the written explanation for you, but you could certainly use the discussed guidance to help in understanding how polynomial division is arranged and the parts of the formal process.  Make use of quotient, divisor dividend, partial quotient, and any other instructive vocabulary that you want to use in your explanation.  Really, you need to know how to do polynomial division, and try to describe the steps precisely/ as precisely as you can do.