#### Answer

(3q+2)(3q+2)

#### Work Step by Step

Given the polynomial
$9q^{2}$ + 12q + 4
*** We break of the middle term into two factors that add to give +12 and multiply to give +36. The two numbers are +6 and +6.
$9q^{2}$ + 6q + 6q + 4
We take the GCD of the first two and the GCD of the last two terms.
3q(3q+2) +2(3q+2)
We take (3q+2) and factor it out which gives us.
(3q+2)(3q+2)