Question

solve for x.
$2x^3 - x^2 - 2x + 1 = 0$
$x = ?, \frac{\quad}{\quad}, \quad$
enter the solutions in ascending order.

Explanation:

Step1: Group terms for factoring

$(2x^3 - x^2) + (-2x + 1) = 0$

Step2: Factor out common terms

$x^2(2x - 1) - 1(2x - 1) = 0$

Step3: Factor out binomial

$(x^2 - 1)(2x - 1) = 0$

Step4: Factor difference of squares

$(x - 1)(x + 1)(2x - 1) = 0$

Step5: Solve for x individually

$x - 1 = 0 \implies x=1$; $x + 1 = 0 \implies x=-1$; $2x - 1 = 0 \implies x=\frac{1}{2}$

Step6: Sort solutions ascendingly

$-1 < \frac{1}{2} < 1$

Answer:

$x = -1, \frac{1}{2}, 1$