[2x^(3)-4x²-15x+5] / [x²-2x-8]
i get 2x with a remainder of x+5...is this right or did i do this wrong?
if it's right how do i write this properly
You're correct. The proper way to write your result is as follows:
$\displaystyle 2x+\dfrac{x+5}{x^{2}-2x-8}.$
Incidentally, you can check your own work by getting a common denominator and adding the two fractions together like this:
$\displaystyle 2x+\dfrac{x+5}{x^{2}-2x-8}=\dfrac{2x}{1}+\dfrac{x+5}{x^{2}-2x-8}=\dfrac{2x(x^{2}-2x-8)}{x^{2}-2x-8}+\dfrac{x+5}{x^{2}-2x-8}\dots$
You should get back to the original fraction.