Question

solve for x.
$x^3 - x^2 - 2x = 0$
$x = ?, , $
enter the solutions in ascending order.

Explanation:

Step1: Factor out common term $x$

$x(x^2 - x - 2) = 0$

Step2: Factor quadratic expression

Find two numbers that multiply to $-2$ and add to $-1$: $-2$ and $1$.
$x(x - 2)(x + 1) = 0$

Step3: Set each factor to 0

$x=0$, $x-2=0$, $x+1=0$

Step4: Solve for $x$

$x=0$, $x=2$, $x=-1$

Step5: Sort solutions ascendingly

$-1 < 0 < 2$

Answer:

$x = -1, 0, 2$