Division of a polynomial

[silverdragon316]

This is my problem:

(4x^4-3x^2+5x-9)/(x^2-3)

................................4x^2.............
x^2-3../4x^2+0x^3-3x^2+5x-9
...........((4x^4.........-12x^2)
...................................9


I know 5x-9 is the remainder but what happens to the 9?

How do I write the answer?

 

[galactus]

You're a little misconstrued.

See if you can get to:

\(\displaystyle \L\\\frac{5x+18}{x^{2}-3}+4x^{2}+9\)

 

[silverdragon316]

Thank you very much.

 

[Denis]

Your division should look like this:

          4x^2 + 9
          ====================
x^2 - 3 / 4x^4 - 3x^2 + 5x - 9
          4x^4 -12x^2
          ===========
                 9x^2 + 5x - 9
                 9x^2      -27
                 =============
                        5x +18