Factor. \( -3 v^{2}-17 v+56 \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. \( -3 v^{2}-17 v+56=\square \) (Factor completely.) B. The trinomial is not factorable.

To factor the expression \( -3 v^{2} - 17 v + 56 \), we begin by looking for two numbers that multiply to \( -3 \times 56 = -168 \) and add up to \( -17 \). The pair of numbers that meet these criteria is \( -21 \) and \( 8 \). Next, we can rewrite the trinomial using these numbers: \[ -3v^{2} - 21v + 8v + 56. \] Now, group the terms: \[ (-3v^{2} - 21v) + (8v + 56). \] Factoring out the common factors from each group results in: \[ -3v(v + 7) + 8(v + 7). \] Now we can factor out the common binomial factor: \[ (v + 7)(-3v + 8). \] So, the complete factorization is: \[ -3v^{2} - 17v + 56 = (v + 7)(-3v + 8). \] Thus, the correct choice is: A. \( -3 v^{2}-17 v+56=(v + 7)(-3v + 8). \) This means you can now confidently move on to tackle similar problems! Remember, factoring is all about finding patterns and common elements. When you're stuck, try rewriting or grouping – it can make all the difference!