Please can you give me a step by step solution of the following 
long division of polynominals question:
3x^4+4x^3-2x^2+8 divided by 2x^3-18x+2x^2-18.

This isn't step-by-step, but if you can't follow it at all
then you need to learn the procedure from simpler examples.
This is too advanced a problem from which to be learning 
the procedure for the first time.

The dividend polynomial 3x4 + 4x3 - 2x2 + 8 is in order of
descending powers of x but it has a missing term in x. So 
we need to insert a place-holder of + 0x and write it as:

3x4 + 4x3 - 2x2 + 0x + 8

The divisor polynomial 2x3 - 18x + 2x2 - 18 is not in
order of descending powers of x so we write it as
2x3 + 2x2 - 18x - 18

                                                    1.5x + .5
            2x3 + 2x2 - 18x - 18) 3x4 + 4x3 -  2x2 +   0x + 8
                                  3x4 + 3x3 - 27x2 -  27x 
                                        x3 + 25x2 +  27x +  8
                                        x3 +   x2 -   9x -  9
                                             24x2 +  36x + 17

Now we write the final answer as

                     remainder
         quotient + ——————————— 
                      divisor

                        24x2 + 36x + 17
        1.5x + .5 + ——————————————————————
                     2x3 + 2x2 - 18x - 18

Edwin