Question

which shows one way to determine the factors of $4x^3 + x^2 - 8x - 2$ by grouping?
\\(\circ\\) $x^2(4x + 1) - 2(4x + 1)$
\\(\circ\\) $x^2(4x - 1) + 2(4x - 1)$
\\(\circ\\) $4x^2(x + 2) - 1(x + 2)$
\\(\circ\\) $4x^2(x - 2) - 1(x - 2)$

Explanation:

Step1: Recall factoring by grouping

To factor \(4x^{3}+x^{2}-8x - 2\) by grouping, we group the first two terms and the last two terms: \((4x^{3}+x^{2})+(-8x - 2)\)

Step2: Factor out GCF from each group

For the first group \(4x^{3}+x^{2}\), the greatest common factor (GCF) is \(x^{2}\). Factoring out \(x^{2}\), we get \(x^{2}(4x + 1)\).

For the second group \(-8x-2\), we can factor out \(- 2\) (since the GCF of \(-8x\) and \(-2\) is \(-2\)). Factoring out \(-2\), we get \(-2(4x + 1)\) (because \(-2\times4x=-8x\) and \(-2\times1 = - 2\)).

So the expression becomes \(x^{2}(4x + 1)-2(4x + 1)\)

Answer:

A. \(x^{2}(4x + 1)-2(4x + 1)\)