Factor completely. If the polynomial is prime, state so. \( x^{2}+12 x+36 \)

The given polynomial is: \[ x^2 + 12x + 36 \] To factor this quadratic, we look for two numbers that multiply to \( 36 \) (the constant term) and add up to \( 12 \) (the coefficient of the middle term). These numbers are \( 6 \) and \( 6 \), since: \[ 6 \times 6 = 36 \quad \text{and} \quad 6 + 6 = 12 \] Thus, the polynomial can be written as: \[ (x + 6)(x + 6) = (x + 6)^2 \] **Final Answer:** \[ (x + 6)^2 \]