Division of Polynomials?

Question

(3x^4 + 2x^3 - 11x^2 - 2x + 5)divided by(x^2 - 2)
Need help with this concept, I have managed to figure everything else out on my own, but I was unable to attend class on the lesson of division of polynomials due to crohn's disease. From reading the textbook and the website purplemath.com I have the basic idea, but when I apply the concept to this question, it doesn't seem to work out, I'm trying to do long division. Any suggestions would be greatly appreciated, an explanation of how to get to the answer would help me to learn this, thanks!!!

Answer 1

.................. 3 x^2 + 2x - 5
...................______________________________________
....(x^2 - 2) | 3x^4 + 2x^3 - 11x^2 - 2x + 5
...................| 3x^4 ...........- 6 x^2
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subtracting |........ + 2x^3 - 5 x^2 - 2x +5
...................|.........+ 2x^3 -------- - 4x
________________________________________________
subtracting | .................... - 5x^2 + 2x + 5
...................| .................... - 5x^2 ........+ 10
________________________________________________
subtracting | ...............................+ 2x - 5
the result = 3 x^2 + 2x - 5
and the remainder = 2x - 5

Answer 2

Divide x^2 into 3x^4 first, then mult by both.
.................3x^2.....+2x..... -5
x^2 - 2 /------------------------------
..............3x^4 +2x^3 -11x^2 -2x + 5
..............3x^4...........- 6x^2 ...............now subtract
_________________________________________
.......................2x^3 - 5x^2 - 2x + 5 Divide again
........................2x^3............-4x
-----------------------------------------
...............................-5x^2 + 2x + 5
..............................-5x^2............+10
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......................2x - 5 is the remainder since you can not divide again