Question

question
factor the expression completely.
-4x³ + 6

Explanation:

Step1: Identify the GCF

Find the greatest common factor (GCF) of \(-4x^3\) and \(6\). The GCF of \(4\) and \(6\) is \(2\), and we can also factor out a negative sign for simplicity. So the GCF is \(-2\) (or \(2\), we'll use \(-2\) here).
\(-4x^3 + 6=-2(2x^3 - 3)\)

Step2: Check for further factoring

The expression \(2x^3 - 3\) is a sum of cubes? No, it's \(2x^3-3\), and since \(3\) is not a perfect cube in terms of \(x\), and there are no common factors or other factoring patterns (like difference of squares, etc.) applicable here, we stop.

Answer:

\(-2(2x^3 - 3)\) (or \(2(-2x^3 + 3)\), but factoring out the negative from the first term is more standard for complete factoring)