Divide. If the polynomial does not divide evenly, include the remainder as a fraction. \( \left(-n^{3}-n^{2}+42 n\right) \div(n+7) \) \begin{tabular}{|l}\( \square \) \\ Submit \end{tabular}

To divide the polynomial \(-n^{3} - n^{2} + 42n\) by \(n + 7\), we perform polynomial long division. ### Division Process: 1. **Divide the leading terms:** \[ \frac{-n^{3}}{n} = -n^{2} \] 2. **Multiply the entire divisor by \(-n^{2}\):** \[ (n + 7) \times (-n^{2}) = -n^{3} - 7n^{2} \] 3. **Subtract this from the original polynomial:** \[ (-n^{3} - n^{2} + 42n) - (-n^{3} - 7n^{2}) = 6n^{2} + 42n \] 4. **Repeat the process with the new polynomial \(6n^{2} + 42n\):** \[ \frac{6n^{2}}{n} = 6n \] 5. **Multiply the divisor by \(6n\):** \[ (n + 7) \times 6n = 6n^{2} + 42n \] 6. **Subtract this from the current polynomial:** \[ (6n^{2} + 42n) - (6n^{2} + 42n) = 0 \] Since the remainder is \(0\), the division is exact. ### Final Answer: \[ -n^{2} + 6n \]