Factor completely. \[ 14 h^{3}-18 h-9+7 h^{2} \]

To factor the expression \( 14h^{3} + 7h^{2} - 18h - 9 \), we can start by rearranging it in standard form: \[ 14h^{3} + 7h^{2} - 18h - 9 \] Next, we'll group the terms: \[ (14h^{3} + 7h^{2}) + (-18h - 9) \] Now, factor out the common factors in each group: 1. From the first group, \( 7h^{2} \) can be factored out: \[ 7h^{2}(2h + 1) \] 2. From the second group, \(-9\) can be factored out: \[ -9(2h + 1) \] Now, we can rewrite the entire expression: \[ 7h^{2}(2h + 1) - 9(2h + 1) \] Next, observe that \((2h + 1)\) is a common factor: \[ (2h + 1)(7h^{2} - 9) \] Now, notice that \( 7h^{2} - 9 \) is a difference of squares, which can be further factored: \[ 7h^{2} - 9 = ( \sqrt{7}h - 3)(\sqrt{7}h + 3) \] Combining everything, we get the completely factored form: \[ (2h + 1)(\sqrt{7}h - 3)(\sqrt{7}h + 3) \] Thus, the completely factored form of the given expression is: \[ \boxed{(2h + 1)(\sqrt{7}h - 3)(\sqrt{7}h + 3)} \]