Question

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

Explanation:

Step1: Group 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:
$$x^2(x - 12) - 2(x - 12)$$

Step3: Match to given options

Compare with the provided choices.

Answer:

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