Question

[(x^3)+(2x^2)-x-2]/(2x-5)

Answer 1

You can use synthetic long division, but you will find that 2x-5 is not a factor of x^3 + 2x^2 -x -2.

You get something like
x^2/2 + (5/4)x + 25/8 + ?/(2x-5)