Factor the trinomial. \[ 2 x^{2} z+14 x z+12 z \] Select the correct choice below and, if necessary, fill in the answer box to comple A. \( 2 x^{2} z+14 x z+12 z=\square \) (Factor completely.) B. \( 2 x^{2} z+14 x z+12 z \) is prime.

To factor the trinomial \( 2 x^{2} z + 14 x z + 12 z \), we start by factoring out the greatest common factor, which is \( 2z \). This gives us: \[ 2z(x^2 + 7x + 6) \] Next, we can factor the quadratic \( x^2 + 7x + 6 \) into \( (x + 1)(x + 6) \). Therefore, the fully factored form of the original trinomial is: \[ 2z(x + 1)(x + 6) \] Now, you have the complete factorization! So, option A: \( 2 x^{2} z+14 x z+12 z = 2z(x + 1)(x + 6) \).