Divide. If the polynomial does not divide evenly, include the remainder as a fraction. \( \left(-6 s^{4}-23 s^{3}-15 s^{2}-70 s-154\right) \div(2 s+7) \) Submit

To divide the polynomial \( -6s^4 - 23s^3 - 15s^2 - 70s - 154 \) by \( 2s + 7 \), we can use polynomial long division. 1. Divide the leading term: \(-6s^4 \div 2s = -3s^3\). 2. Multiply \( -3s^3 \) by \( 2s + 7 \): \( -6s^4 - 21s^3 \). 3. Subtract: \( (-6s^4 - 23s^3) - (-6s^4 - 21s^3) = -2s^3 \). 4. Bring down the next term: \( -2s^3 - 15s^2 \). 5. Divide: \(-2s^3 \div 2s = -s^2\). 6. Multiply: \(-s^2(2s + 7) = -2s^3 - 7s^2\). 7. Subtract: \( (-2s^3 - 15s^2) - (-2s^3 - 7s^2) = -8s^2 \). 8. Bring down the next term: \( -8s^2 - 70s \). 9. Divide: \(-8s^2 \div 2s = -4s\). 10. Multiply: \(-4s(2s + 7) = -8s^2 - 28s\). 11. Subtract: \( (-8s^2 - 70s) - (-8s^2 - 28s) = -42s \). 12. Bring down the next term: \( -42s - 154 \). 13. Divide: \(-42s \div 2s = -21\). 14. Multiply: \(-21(2s + 7) = -42s - 147\). 15. Subtract: \( (-42s - 154) - (-42s - 147) = -7 \). So the answer is: \[ -3s^3 - s^2 - 4s - 21 - \frac{7}{2s + 7} \]