Question

$2x^{2}+5x + 2$

Explanation:

Step1: Split middle term

Rewrite $5x$ as $4x + x$
$2x^2 + 4x + x + 2$

Step2: Group terms

Pair first two and last two terms
$(2x^2 + 4x) + (x + 2)$

Step3: Factor out GCFs

Factor $2x$ from first group, 1 from second
$2x(x + 2) + 1(x + 2)$

Step4: Factor common binomial

Extract $(x + 2)$ from both terms
$(2x + 1)(x + 2)$

Answer:

$(2x + 1)(x + 2)$