Solve the equation x^3 - 2x^2 - x + 2 = 0

To solve the equation, we'll group the first 2 terms together and the next 2 terms together, so that we can factorize:

(x^3 - 2x^2) - (x - 2) = 0

x^2(x - 2) - (x - 2) = 0

We'll factorize again:

(x - 2)(x^2 - 1) = 0

We'll put each factor as being 0.

x-2 = 0

x = 2

x^2 - 1 = 0

The expression is a difference of squares:

x^2 - 1 = (x - 1)(x + 1) = 0

x-1 = 0

x = 1

x + 1 = 0

x = -1

The solutions of the equation are: {-1,1,2}.