Question

factor:
$2x^2 + 5x + 2 = \square$
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Explanation:

Step1: Identify coefficients

Quadratic: $2x^2 + 5x + 2$, so $a=2$, $b=5$, $c=2$.

Step2: Find product $ac$

$ac = 2×2 = 4$.

Step3: Split middle term

Find two numbers: product=4, sum=5 → 4 and 1. Split $5x$ into $4x + x$.

Step4: Factor by grouping

$2x^2 + 4x + x + 2 = 2x(x + 2) + 1(x + 2) = (2x + 1)(x + 2)$.

Answer:

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