Question

factor by grouping. \\(2v^3 + 5v^2 + 12v + 30\\)

Explanation:

Step1: Group terms into pairs

Group the first two and last two terms:
$(2v^3 + 5v^2) + (12v + 30)$

Step2: Factor out GCF from each pair

Factor $v^2$ from first group, 6 from second:
$v^2(2v + 5) + 6(2v + 5)$

Step3: Factor out common binomial

Extract $(2v + 5)$ from both terms:
$(2v + 5)(v^2 + 6)$

Answer:

$(2v + 5)(v^2 + 6)$