Question

which shows one way to determine the factors of $x^3 - 12x^2 - 2x + 24$ by grouping?\
\\(\bigcirc\\) $x(x^2 - 12) + 2(x^2 - 12)$\
\\(\bigcirc\\) $x(x^2 - 12) - 2(x^2 - 12)$\
\\(\bigcirc\\) $x^2(x - 12) + 2(x - 12)$\
\\(\bigcirc\\) $x^2(x - 12) - 2(x - 12)$

Explanation:

Step1: Group the polynomial terms

Group first two and last two terms:
$(x^3 - 12x^2) + (-2x + 24)$

Step2: Factor out GCF from each group

Factor $x^2$ from first group, $-2$ from second group:
$x^2(x - 12) - 2(x - 12)$

Answer:

$x^2(x - 12) - 2(x - 12)$