Divide. If the polynomial does not divide evenly, include the remainder as a fraction \( \left(-36 t^{3}+49 t\right) \div(6 t+7) \) Submit

To divide the polynomial \(-36t^{3} + 49t\) by \(6t + 7\), we can use polynomial long division. 1. Divide the leading term: \(-36t^3\) by \(6t\) gives us \(-6t^2\). 2. Multiply \(-6t^2\) by \(6t + 7\): \(-6t^2 \cdot (6t + 7) = -36t^3 - 42t^2\). 3. Subtract this from the original polynomial: \[ (-36t^3 + 49t) - (-36t^3 - 42t^2) = 42t^2 + 49t. \] 4. Now repeat this process with \(42t^2 + 49t\). 5. Divide \(42t^2\) by \(6t\) to get \(7t\). 6. Multiply \(7t\) by \(6t + 7\): \(7t \cdot (6t + 7) = 42t^2 + 49t\). 7. Subtract again: \[ (42t^2 + 49t) - (42t^2 + 49t) = 0. \] Since there is no remainder in this division, the final result is: \[ -6t^2 + 7t. \] Thus, the complete answer is: \(-6t^2 + 7t\) (no remainder).