Factor the following completely. \( -50 w^{3}-20 w^{2}+48 w \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. \( -50 w^{3}-20 w^{2}+48 w= \) (Type your answer in factored form.) B. The trinomial is not factorable.

First, let's identify the greatest common factor (GCF) of the terms in the polynomial, which is \( -2w \). Factoring this out gives: \[ -50 w^{3}-20 w^{2}+48 w = -2w(25w^{2} + 10w - 24) \] Now, we need to factor the quadratic \( 25w^{2} + 10w - 24 \). Using the quadratic formula or by grouping, we arrive at: \[ -2w(25w^{2} + 10w - 24) = -2w(5w - 6)(5w + 4) \] Therefore, the final factored form is: \[ -50 w^{3}-20 w^{2}+48 w = -2w(5w - 6)(5w + 4) \] This brings us to option A.