Answer
{-1, 1, 2}
Work Step by Step
1. Rearrange expression to equal zero.
$x^{3}$ - x = 2$x^{2}$ - 2
$x^{3}$ - x - 2$x^{2}$ + 2 = 0
2. Factor the expression.
x($x^{2}$ - 1) - 2($x^{2}$ - 1)
(x - 2)($x^{2}$ - 1)
(x - 2)(x + 1)(x - 1)
3. Apply the zero factor property.
a) x - 2 = 0
b) x + 1 = 0
c) x - 1 = 0
4. Solve each linear equation.
a) x = 2
b) x = -1
c) x = 1
The solutions are {-1, 1, 2}.
