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

Factor the expression \( 4b^5+12b^2-5b^3-15 \). Factor the expression by following steps: - step0: Factor: \(4b^{5}+12b^{2}-5b^{3}-15\) - step1: Rewrite the expression: \(4b^{2}\times b^{3}+4b^{2}\times 3-5b^{3}-5\times 3\) - step2: Factor the expression: \(4b^{2}\left(b^{3}+3\right)-5\left(b^{3}+3\right)\) - step3: Factor the expression: \(\left(4b^{2}-5\right)\left(b^{3}+3\right)\) The factored form of the given polynomial \(4b^{5}+12b^{2}-5b^{3}-15\) is \((4b^{2}-5)(b^{3}+3)\).