I can't figure this out

Rational root theorem

X^3 - x^2 + 2x - 2 = 0

for x = 1, (1) ^3 - (1) ^2 + 2 (1) - 2 = 0

Thus x - 1 is a factor.

Dividing x^3 - x^2 + 2x - 2 by x - 1 gives x^2 + 2 which does not have real factors.

The factor of x^2 + 2 = (x - i√2) (x + i√2)

Therefore, The roots of x^3 - x^2 + 2x - 2 are x = 1, x = i√2 and x = - i√2