Divide. If the polynomial does not divide evenly, include the remainder as a fraction. \( \left(-2 z^{3}+8 z^{2}+47 z-35\right) \div(z-7) \) Submit

To divide the polynomial \(-2z^{3}+8z^{2}+47z-35\) by \(z-7\), we can use synthetic division or polynomial long division. We'll proceed with synthetic division, using \(7\) (the zero of \(z-7\)). Setting up synthetic division: ``` 7 | -2 8 47 -35 | -14 -42 35 ----------------------- -2 -6 5 0 ``` The coefficients represent the result of the division, where the quotient is \(-2z^2 - 6z + 5\) with a remainder of \(0\). Thus, the division results in: \[ -2z^{2} - 6z + 5 \] Since the remainder is \(0\), the polynomial divides evenly.