Question

question
factor the expression completely.
$6x^5 - x^3$

Explanation:

Step1: Identify greatest common factor

The terms $6x^5$ and $x^3$ share $x^3$ as the greatest common factor.

Step2: Factor out the GCF

$$\begin{align*} 6x^5 - x^3 &= x^3(6x^2) - x^3(1) \\ &= x^3(6x^2 - 1) \end{align*}$$

Step3: Check for further factoring

The quadratic $6x^2 - 1$ cannot be factored over integers, so we stop here.

Answer:

$x^3(6x^2 - 1)$