Factor by grouping. Select "Prime" if the polynomial cannot be factored. \( 4 b^{5}+12 b^{2}-5 b^{3}-15=\square \) \( \square \)

To factor the polynomial \( 4b^5 + 12b^2 - 5b^3 - 15 \) by grouping, we can rearrange the terms as \( (4b^5 - 5b^3) + (12b^2 - 15) \). Factoring out the common factors from each group gives us \( b^3(4b - 5) + 3(4b - 5) \). Now we can see that \( (4b - 5) \) is a common factor, leading to the final factored form: \( (4b - 5)(b^3 + 3) \). So, the answer will be: \( (4b - 5)(b^3 + 3) \)