Question

question
factor the expression completely.
$3x^3 - 10x$

Explanation:

Step1: Identify the greatest common factor (GCF)

The terms in the expression \(3x^3 - 10x\) are \(3x^3\) and \(-10x\). The GCF of the coefficients \(3\) and \(10\) is \(1\), and the GCF of the variable parts \(x^3\) and \(x\) is \(x\). So the GCF of the two terms is \(x\).

Step2: Factor out the GCF

Factor out \(x\) from each term:
\(3x^3 - 10x = x(3x^2 - 10)\)
Now, check if \(3x^2 - 10\) can be factored further. Since \(3x^2 - 10\) is a difference of squares? No, because \(3x^2\) is not a perfect square (in terms of rational coefficients) and \(10\) is not a perfect square times \(3\). So we stop here.

Answer:

\(x(3x^2 - 10)\)