SOLUTION: 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

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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