Question

1. $8x^{2}+20x+8$

Explanation:

Step1: Factor out GCF

$\gcd(8,20,8)=4$, so:
$8x^2 + 20x + 8 = 4(2x^2 + 5x + 2)$

Step2: Factor quadratic trinomial

Find two numbers that multiply to $2\times2=4$ and add to $5$ (4 and 1). Split the middle term:
$2x^2 + 4x + x + 2 = 2x(x+2) + 1(x+2) = (2x+1)(x+2)$

Step3: Combine factors

Substitute back into the expression from Step1:
$4(2x+1)(x+2)$

Answer:

$4(2x+1)(x+2)$