Factorize $x^3-3x+2$ How can I factorize $x^3-3x+2$ ?
The answer that I got on the internet is $x^3-2x^2+x+2x^2-4x+2$=$(x-1)^2(x+2)$ 
It would be nice if anyone could also tell what these type of equations are called and where can I learn more?

Just in case you're wondering what is meant by a rational "root": a root for a given polynomial can be thought of as a value $r$ such that when you set $x = r$, the value of the polynomial evaluates to zero.  Some people refer to the roots as the "zeros" of a polynomial.
So, I'll use $P(x)$ to denote the equation $x^3-3x+2$; that is, we have
$$P(x) = x^3 - 3x + 2 = (x-1)^2(x+2)$$
Now, when is $P(x) = 0$?
When $(x-1)=0$ and/or when $(x+2)=0$, because when that happens, then $$P(x) = (0)(x+1) =0\ \text{or}\ P(x) =(x-1)^2(0) = 0$$
Now we simply solve for $x$ to find the roots:
$(x-1) = 0\implies x=1$, so $1$ is a root of $P(x)$, and
$(x+2) = 0 \implies x = -2$, so $-2$ is a root of $P(x)$,
and, voila, you have the roots, as given in the first answer.
In terms of learning how to factor a polynomial, the best advice I have to offer is practice!
