Factor. \( 2 x^{2}-x-15 \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. \( 2 x^{2}-x-15=\square \) (Factor completely.) B. The trinomial is not factorable.

To factor the expression \( 2x^2 - x - 15 \), we look for two numbers that multiply to \( 2 \times -15 = -30 \) and add to \( -1 \) (the coefficient of \( x \)). These two numbers are \( 5 \) and \( -6 \). Rewriting the middle term, we have: \( 2x^2 + 5x - 6x - 15 \). Now, we can factor by grouping: \( x(2x + 5) - 3(2x + 5) = (2x + 5)(x - 3) \). So, \( 2x^2 - x - 15 = (2x + 5)(x - 3) \). Now we can check our work by expanding the factors: \( (2x + 5)(x - 3) = 2x^2 - 6x + 5x - 15 = 2x^2 - x - 15 \), confirming that it factors correctly! Therefore, the completed factorization is \( (2x + 5)(x - 3) \).