Question 882930: a Polynomial P(x) and a divisor d(x) are given. Use long division to find the quotient Q(x) and the remainder R(x) when P(x) is divided by d(x), and express P(x) in the form d(x)*Q(x)+R(x)
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! THE SOLUTION:
 ,  , and P(x) in the form d(x)*Q(x)+R(x), or
 , is  .
THE LONG DIVISION:
The format for long division varies from country to country (and maybe even from teacher to teacher. I will use the format my children were taught in the USA.
The first term of quotient  is the quotient of the first terms  .
Then  is subtracted from .
Subtracting  is adding  ,
and the result is
 .
That is shown below, but I am saving room for terms in  by including the term  .
 --->
We continue dividing by  the remaining  ,
which I wrote as  to save room for the term in .
The next term in the quotient, which comes from dividing first terms, is
 .
That term, times the divisor is
 , which must be subtracted from
 .
Subtracting  is adding  ,
and the result is  .
 --->
To find the next term of ,
we have to divide the first term of the remaining 
by the first term of divisor  :
 .
So the last term of the quotient will be   ,
and we need to subtract the product
 from the remaining .
Since subtracting  is adding  ,
I add  to that remaining and find the remainder:
 :
 --->
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