Factor. \[ w^{2}+12 w+36 \] Select the correct choice below and fill in any answer box within your choice. A. $w^{2}+12 w+36=\square$ B. $w^{2}+12 w+36$ is prime.

Step 1 ：Given the expression \(w^{2}+12 w+36\).

Step 2 ：Recognize that this is a perfect square trinomial.

Step 3 ：The factors of 36 that add up to 12 are 6 and 6.

Step 4 ：Therefore, the expression can be factored as \((w+6)^2\).

Step 5 ：So, \(w^{2}+12 w+36=(w+6)^2\).