Factor the following trinomial. \[ x^{2}+8 x+15 \] Select the correct choice below and, if ne A. \( x^{2}+8 x+15=\square \) (Type your ans B. The polynomial is prime.

1. We start with the trinomial \[ x^{2}+8 x+15. \] 2. We look for two numbers that multiply to \(15\) (the constant term) and add up to \(8\) (the coefficient of \(x\)). - The numbers \(3\) and \(5\) satisfy this: \[ 3 \times 5 = 15 \quad \text{and} \quad 3 + 5 = 8. \] 3. Using these numbers, we can factor the trinomial as: \[ x^{2}+8 x+15 = (x+3)(x+5). \] The correct choice is: A. \( x^{2}+8 x+15=(x+3)(x+5) \).