Question

factor the expression completely. $5x^3 - x$

Explanation:

Step1: Factor out common term

Identify the greatest common factor of $5x^3$ and $x$, which is $x$.
$5x^3 - x = x(5x^2 - 1)$

Step2: Check for further factoring

The expression $5x^2 - 1$ is a difference of squares (since $5x^2 = (\sqrt{5}x)^2$ and $1 = 1^2$), so factor it using $a^2 - b^2=(a-b)(a+b)$.
$x(5x^2 - 1) = x(\sqrt{5}x - 1)(\sqrt{5}x + 1)$

Answer:

$x(\sqrt{5}x - 1)(\sqrt{5}x + 1)$