Question

question
factor the expression completely.
$3x^3 + 7x$

Explanation:

Step1: Identify the GCF

Find the greatest common factor (GCF) of \(3x^3\) and \(7x\). The GCF of the coefficients \(3\) and \(7\) is \(1\), and the GCF of the variable terms \(x^3\) and \(x\) is \(x\). So the GCF is \(x\).

Step2: Factor out the GCF

Factor out \(x\) from each term: \(3x^3 + 7x = x(3x^2 + 7)\)

Step3: Check if further factoring is possible

The quadratic \(3x^2 + 7\) has a discriminant \(b^2 - 4ac = 0^2 - 4(3)(7) = -84\), which is negative, so it doesn't factor over the real numbers.

Answer:

\(x(3x^2 + 7)\)