How do you divide polynomials using long division

This is a simple example:-
             x   +   9
         
x - 1 )  x^2  +  8x  -    9
           x^2  -   x                  subtract
           
                     9x  -  9
                     9x  -  9
                 
                     

First divide x into x^2  to give x which goes above 
Then multiply x - 1 by x to give x^2 - x

Subtract this fro x^2 + 8x  gives 9x
Bring down the - 9 then divide x into 9x
and finally  multiply x - 1 by  9 to give   9x - 9
Finally subtract  and you sre done. There is no remainder as x - 1 is a factor of x^2 + 8x - 9.

The  polynomial must be in descending powers of x . If one is missing you insert it  with a coefficient of zero before you start the division. 

for example if you have   x^3 - 3x + 12   you write it as

 x^2 + 0x^2 - 3x + 12