I don't quite understand what I have to do so I would really appreciate any help

The questions is "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). Express in the form P(x)=d(x)*q(x)+R(x)

P(x)=x^3 -27

d(x)=x+3

$\small{ \begin{array}{rcl} (x^3-27) : ( x+3) &=& x^2 - 3x + 9 - \frac{54}{x+3} \qquad | \qquad \cdot (x+3) \\ (x^3-27) &=& ( x+3)( x^2 - 3x + 9 ) -54 \\ \end{array} }$

It is difficult to lay this out properly on the forum but it is quite literally done the same as a number long division.

I'll see if I can find another example :/

Here is one example :/

http://web2.0calc.com/questions/3x-3-5x-2-10x-3-3x-4

If you google "Algebraic long division"  There are a heap of sites and more than one good you tube clip that deals with this topic.  

               x^2   - 3x    + 9

x + 3   [   x^3  - 0x^2   - 0x   - 27 ]

              x^3  + 3x^2

           ---------------------------------

                       -3x^2  - 0x

                      -3x^2  -  9x

                     ------------------

                                    9x   -  27

                                    9x  +  27

                                  --------------

                                          - 54

So...we have     [ x ^3 - 27 ] =  [x + 3] *   [ x^2 - 3x + 9]   - 54