Divide. If the polynomial does not divide evenly, include the remainder as a fraction. \[ (81 r+68) \div(9 r+7) \]

To divide the polynomial \( 81r + 68 \) by \( 9r + 7 \), follow these steps: 1. **Determine the Quotient:** - Divide the leading term of the dividend by the leading term of the divisor: \[ \frac{81r}{9r} = 9 \] - So, the initial quotient is **9**. 2. **Multiply and Subtract:** - Multiply the entire divisor by the quotient: \[ 9 \times (9r + 7) = 81r + 63 \] - Subtract this from the original dividend: \[ (81r + 68) - (81r + 63) = 5 \] 3. **Express the Final Result:** - The remainder is **5**, which is less than the degree of the divisor \( 9r + 7 \). - Therefore, the division can be expressed as: \[ \frac{81r + 68}{9r + 7} = 9 + \frac{5}{9r + 7} \] **Final Answer:** \[ \frac{81 r + 68}{9 r + 7} = 9 + \frac{5}{9 r + 7} \]