Question 10851
{{{x^3 - 2x^2 + x - 2 = 0}}} Factor.

{{{(x - 2)(x^2 + 1) = 0}}} Apply the zero product principle.

{{{x - 2 = 0}}} or {{{x^2 + 1 = 0}}}

If {{{x = -2}}} then {{{x = 2}}} A real root.

If {{{x^2 + 1 = 0}}} then {{{x^2 = -1}}} and x = +-{{{sqrt(-1)}}} Two imaginary roots.