Divide. If the polynomial does not divide evenly, include the remainder as a fraction. \( \left(-18 d^{4}+27 d^{3}+28 d^{2}-20 d\right) \div(d-2) \)

To divide the polynomial \(-18 d^{4}+27 d^{3}+28 d^{2}-20 d\) by \(d-2\), we can use synthetic division or polynomial long division. Using synthetic division: 1. We first substitute \(2\) (the root of \(d - 2\)) into the coefficients: \([-18, 27, 28, -20, 0]\). 2. Bring down \(-18\). 3. Multiply \(2\) by \(-18\) (which is \(-36\)) and add to \(27\): \(27 + (-36) = -9\). 4. Multiply \(2\) by \(-9\) (which is \(-18\)) and add to \(28\): \(28 + (-18) = 10\). 5. Multiply \(2\) by \(10\) (which is \(20\)) and add to \(-20\): \(-20 + 20 = 0\). So, we have no remainder. The result of the division is \(-18d^{3} - 9d^{2} + 10\). Final Answer: \(-18 d^{3}-9 d^{2}+10\) with a remainder of \(0\).