Question

factor completely. \\(2x^3 + 7x^2 + 50x + 175\\)

Explanation:

Step1: Group terms into pairs

Group first two and last two terms:
$(2x^3 + 7x^2) + (50x + 175)$

Step2: Factor out GCF from each group

Factor $x^2$ from first pair, 25 from second pair:
$x^2(2x + 7) + 25(2x + 7)$

Step3: Factor out common binomial

Factor $(2x + 7)$ from both terms:
$(2x + 7)(x^2 + 25)$

Answer:

$(2x + 7)(x^2 + 25)$