Math question: factoring

x^3+x-2 -----------(-2)拆成-1-1
=x^3-1 +x-1
=(x-1)(x^2+x+1)+(x-1)
=(x-1)(x^2+x+1+1)
=(x-1)(x^2+x+2)

Using Factor Theorem, put x = 1, the expression = (1)^3 + (1) - 2 = 0, that means (x - 1) is a factor. So the expression becomes
(x - 1)(x^2 + 2 + x).