Question

factor $-8x^3 - 2x^2 - 12x - 3$ by grouping. what is the resulting expression?\
\bigcirc $(2x^2 - 3)(4x + 1)$\
\bigcirc $(-2x^2 - 3)(-4x + 1)$\
\bigcirc $(2x^2 - 3)(-4x + 1)$\
\bigcirc $(-2x^2 - 3)(4x + 1)$

Explanation:

Step1: Group terms into pairs

Group the first two and last two terms:
$(-8x^3 - 2x^2) + (-12x - 3)$

Step2: Factor out GCF from each pair

Factor $-2x^2$ from first group, $-3$ from second group:
$-2x^2(4x + 1) - 3(4x + 1)$

Step3: Factor out common binomial

Factor out $(4x + 1)$ from both terms:
$(-2x^2 - 3)(4x + 1)$

Step4: Verify match with options

Compare the result to the given choices.

Answer:

$(-2x^2 - 3)(4x + 1)$