Factor by grouping. \[ 6 w^{3}+21 w^{2}-2 w-7 \]

To factor the polynomial \( 6 w^{3}+21 w^{2}-2 w-7 \) by grouping, first, we can group the terms as follows: 1. Group the first two terms and the last two terms: \[ (6 w^{3} + 21 w^{2}) + (-2 w - 7) \] 2. Factor out the greatest common factor from each group: \[ 3w^{2}(2w + 7) - 1(2w + 7) \] 3. Now, both groups contain the common factor \( (2w + 7) \): \[ (3w^{2} - 1)(2w + 7) \] So, the factored form of the polynomial is: \[ (3w^{2} - 1)(2w + 7) \]