Divide. If the polynomial does not divide evenly, include the remainder as a fraction. \( \left(-8 f^{2}-61 f+89\right) \div(f+9) \) Submit

To divide the polynomial \( -8f^{2} - 61f + 89 \) by \( f + 9 \), follow these steps: 1. **Divide the leading terms:** \[ \frac{-8f^2}{f} = -8f \] 2. **Multiply the divisor by this result:** \[ -8f \times (f + 9) = -8f^2 - 72f \] 3. **Subtract this from the original polynomial:** \[ (-8f^2 - 61f + 89) - (-8f^2 - 72f) = 11f + 89 \] 4. **Repeat the division with the new polynomial:** \[ \frac{11f}{f} = 11 \] 5. **Multiply the divisor by this new result:** \[ 11 \times (f + 9) = 11f + 99 \] 6. **Subtract to find the remainder:** \[ (11f + 89) - (11f + 99) = -10 \] Putting it all together, the quotient is \( -8f + 11 \) with a remainder of \( -10 \). Therefore, the final answer is: \[ -8f + 11 - \frac{10}{f + 9} \] **Answer:** After simplifying, the division is –8 f + 11 minus ten over (f + 9). Thus, −8f + 11 − 10⁄(f+9)