Question

factor completely.\\(4x^{3}+x^{2}+64x + 16\\)

Explanation:

Step1: Group terms for factoring

Group the polynomial into two pairs:
$(4x^3 + x^2) + (64x + 16)$

Step2: Factor out GCF from each group

Factor $x^2$ from the first pair and 16 from the second pair:
$x^2(4x + 1) + 16(4x + 1)$

Step3: Factor out common binomial

Factor out the shared binomial $(4x + 1)$:
$(4x + 1)(x^2 + 16)$

Answer:

$(4x + 1)(x^2 + 16)$