jmc

The long division is shown below.

$$\begin{array}{ccccc}\text{multicolumn}2r7x^2& -11x& +17& & \\ \text{cline}2-5x+2& 7x^3& +3x^2& -5x& -8\\ \text{multicolumn}2r7x^3& +14x^2& & & \\ \text{cline}2-3\text{multicolumn}2r& -11x^2& -5x& & \\ \text{multicolumn}2r& -11x^2& -22x& & \\ \text{cline}3-4\text{multicolumn}2r& & +17x& -8& \\ \text{multicolumn}2r& & +17x& +34& \\ \text{cline}4-5\text{multicolumn}2r& & & -42& \end{array}$$Thus, the quotient is $\boxed{7x^2-11x+17}.$