Question

factor completely.
$64x^3 + 48x^2 - 4x - 3$

Explanation:

Step1: Group terms for factoring

Group first two and last two terms:
$(64x^3 + 48x^2) + (-4x - 3)$

Step2: Factor out GCF from groups

Factor $16x^2$ from first group, $-1$ from second:
$16x^2(4x + 3) - 1(4x + 3)$

Step3: Factor out common binomial

Factor $(4x + 3)$ from both terms:
$(4x + 3)(16x^2 - 1)$

Step4: Factor difference of squares

Rewrite $16x^2-1$ as $(4x)^2-1^2$, factor:
$(4x + 3)(4x - 1)(4x + 1)$

Answer:

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