How to factor quadratic $ax^2+bx+c$? How do I shorten this? How do I have to think?
$$ x^2 + x - 2$$
The answer is 
 $$(x+2)(x-1)$$
I don't know how to get to the answer systematically. Could someone explain?
Does anyone have a link to a site that teaches basic stuff like this? My book does not explain anything and I have no teacher; this is self-studies.
Please help me out; thanks!

Given 

$$A: x^2 + x - 2$$

you're trying to do the 'magic' in your head in order to get backwards to 

$$B: (x+2)(x-1)$$ 

What is it that you are trying to do backwards. It's the original multiplication of $(x+2)(x-1)$. Note that 


*

*the -2 in $A$ comes from multiplying the +2 and -1 in $B$

*the +1 (it's kind of invisible it's the coefficient of $x$ ) in  $B$ comes from:

*

*$x$ in the first part times -1 in the second, plus 

*+2 in the first part times $x$ in the second



or $(-1)+2 = +1$.
So that's how the multiplication works going forward. Now you have to think of that to go backwards. In $x^2 + x - 2$:


*

*where does the -2 come from? From two things that multiply to get -2. What could those possibly be? Usually we assume integers so the only possibilities are the two pairs 2, -1, and -2, 1.

*of those two pairs, they have to -add- to the coefficient for $x$ or just plain positive 1. So the answer has to be the pair 2 and -1.


Another example might help: given 

$$x^2-5x+6$$

what does this factor to? (that is, find $(x-a)(x-b)$ which equals $x^2 -5x + 6$).
So the steps are:


*

*what are the factors of 6? (you should get 2 pairs, all negative.

*for those pairs, which pair adds up to -5?


The main difficulty is keeping track in your head of what is multiplying, what is adding, and what is positive and negative. 
The pattern for any sort of problem solving skill like this that seems like magic (but really is not) is to:


*

*Do more examples to get a speedier feel for it.

*Check your work. Since you're going backwards, once you get a possible answer, you can do the non-magic (multiplying) to see if you can get the original item in the question.

