Question

factor by grouping.
\\(4u^3 + 7u^2 + 8u + 14\\)

Explanation:

Step1: Group terms into pairs

Group the first two and last two terms:
$(4u^3 + 7u^2) + (8u + 14)$

Step2: Factor out GCF from each pair

Factor $u^2$ from first group, 2 from second:
$u^2(4u + 7) + 2(4u + 7)$

Step3: Factor out common binomial

Factor out $(4u + 7)$ from both terms:
$(4u + 7)(u^2 + 2)$

Answer:

$(4u + 7)(u^2 + 2)$