Expert: Scott A Wilson - 4/13/2011

Question
how do u divide (4x^3-3x^4+5x^3-6x^2-8x+10)/(2x^2)

Answer
Apply it to each term.  Dividing by 2 is just dividing by 2.
Dividing by x^2 means subtracting 2 from the exponet.

To divide 4x^3 by 2x^2 means to take 4/2 = 2 and x^3/x^2 and get x,
so for the first one, it is 2x.

Looking at the entire problem, though, it looks like the powers on x are decreasing,
so that should really be (4x^5-3x^4+5x^3-6x^2-8x+10)/(2x^2).
Note that the first exponet is changed to 5, not 3, as the rest are 4, 3, 2, ...

Now (4x^5-3x^4+5x^3-6x^2-8x+10)/(2x^2) is really
4x^5/(2x^2) - 3x^4/(2x^2) + 5x^3/(2x^2) - 6x^2/(2x^2) - 8x/(2x^2) + 10/(2x^2).
That is (4/2)x^(5-2) - (3/2)x^(4-2) + (5/2)x^(3-2) - (6/2)x^(2-2) - (8/2)x^(1-2) + (10/2)x^(0-2).
Computed gives you 2x^3 - 1.5x^2 + 2.5x - 3x^0 - 4x^-1 + 5x^-2.

Now x^0 = 1 and x^-n = 1/x^n, so this can be written as
2x^3 - 1.5x^2 + 2.5x - 3 - 4/x + 5/x^2.