Can someone please help me with math?

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I am not really good at Mathematics, but I need it to study Informatics. I understand the exercises, but not the logic behind it, therefore I memorize how to do the exercises instead. The problem is, I don't understand one of the exercises, and the book didn't explain. I don't know what it's called in English, but directly translated I'm supposed to "shorten the expressions" xD.

X^3 + X - 2
--------------
X - 1

The answer is X+2, I got the same answer, but by accident. I don't think it's right. If it had said

X^3 - 2X^2 -5X + 6
-----------------------
X - 3

it would have been much easier, but I don't know what to do when it says X^3 and is missing a X^2. I am sorry about the poor English, it is difficult enough to math in my own language. I wish I was good at math, because I actually think it's interesting, and I like to do the exercises, but since I don't understand the logic, it's difficult when something new is introduced and not explained. I would appreciate it if someone could explain this to me. Thank you.

That would be x^2 + 2

I have all the answers, but I don't know how to solve it.

I think it is called factorization of polynomials: http://en.wikipedia.org/wiki/Factorization#AC_Method or http://tutorial.math.lamar.edu/Classes/ ... oring.aspx

In your first example, it might help to write it as:

X^3 + 0X^2 + X - 2
---------------------------
X - 1

which can be expanded to:

(X^2 + X + 2) (X - 1)
-----------------------------
X - 1

This is based on the guess that (X - 1) is going to form part of the solution, and cancel out on top and bottom. So the result should be X^2 + X + 2

If you want to enjoy algebra, then try some computer-based computation systems like Mathcad (or Maxima, Octave, Scilab) where you can both automatically solve mathematics problems and pick apart the steps involved in the solutions. http://blog.interlinked.org/science/ope ... grams.html

Thank you very much

Purplemath.com is also a good resource for math at this level.

Can't believe nobody's suggested Wolfram. Go ahead, ask it a question - I dare you.

Ooh, thank you! I've bookmarked them.

Wow, I never realised that you could do this kind of thing online! The answer to Yamha's original question: http://www.wolframalpha.com/input/?i=%28X^3+%2B+X+-+2%29+%2F+%28X+-+1%29