Question

question
factor completely:
$4x^2(x^2 + 4) - 3(x^2 + 4)$

Explanation:

Step1: Identify common factor

Both terms have a common factor of \((x^2 + 4)\). Factor it out.
\(4x^2(x^2 + 4) - 3(x^2 + 4) = (x^2 + 4)(4x^2 - 3)\)

Step2: Check for further factoring

The expressions \(x^2 + 4\) and \(4x^2 - 3\) cannot be factored further over the real numbers (since \(x^2 + 4\) has no real roots and \(4x^2 - 3\) factors to \((2x - \sqrt{3})(2x + \sqrt{3})\) over the reals, but if we consider only integer coefficients, it's already factored as is from the previous step with integer coefficients).

Answer:

\((x^2 + 4)(4x^2 - 3)\)