Factor over the Complex Numbers x^3-2x^2+x-2

$x^{3} - 2 x^{2} + x - 2$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(x^{3} - 2 x^{2}) + x - 2$

Factor out the greatest common factor (GCF) from each group.

$x^{2} (x - 2) + 1 (x - 2)$

Factor the polynomial by factoring out the greatest common factor, $x - 2$ .

$(x - 2) (x^{2} + 1)$

Multiply the constant in the polynomial $x^{2} + 1$ by $- i^{2}$ where $i^{2}$ is equal to $- 1$ .

$(x - 2) (x^{2} - 1 i^{2})$

Factor.

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - i^{2} = (a + i) (a - i)$ where $a = x$ and $i = i$ .

$(x - 2) ((x + i) (x - i))$

Remove unnecessary parentheses.

$(x - 2) (x + i) (x - i)$