Divide. If the polynomial does not divide evenly, include the remainder as a fraction. \( \left(64 d^{2}-88 d+20\right) \div(8 d-7) \) Submit

To divide the polynomial \(64d^2 - 88d + 20\) by \(8d - 7\), we can use polynomial long division. Let's perform the division step by step. First, we divide the leading term of the polynomial by the leading term of the divisor: \[ \frac{64d^2}{8d} = 8d \] Now, we multiply the divisor by \(8d\) and subtract it from the polynomial: \[ 64d^2 - 88d + 20 - (8d \cdot 8d - 8d \cdot 7) = 64d^2 - 88d + 20 - (64d^2 - 56d) = 20 - 32d \] Now, we bring down the next term, which is \(20\), and divide it by the divisor: \[ \frac{20}{8d} = \frac{5}{2d} \] Since \(20\) is not divisible by \(8d\), the division stops here, and we have a remainder. The quotient is \(8d - 4\), and the remainder is \(\frac{5}{2d}\). Therefore, the division of \(64d^2 - 88d + 20\) by \(8d - 7\) is: \[ \frac{64d^2 - 88d + 20}{8d - 7} = 8d - 4 + \frac{5}{2d} \] This means that the polynomial \(64d^2 - 88d + 20\) does not divide evenly by \(8d - 7\), and the quotient is \(8d - 4\) with a remainder of \(\frac{5}{2d}\).