Question

1. $4m^{3}+8m^{2}+3m$

Explanation:

Step1: Factor out common term

$4m^3 + 8m^2 + 3m = m(4m^2 + 8m + 3)$

Step2: Factor quadratic trinomial

Find two numbers that multiply to $4\times3=12$ and add to $8$: $2$ and $6$. Split the middle term:
$4m^2 + 2m + 6m + 3 = 2m(2m+1) + 3(2m+1) = (2m+1)(2m+3)$

Step3: Combine all factors

Substitute back into the expression from Step1.

Answer:

$m(2m+1)(2m+3)$