For all of the following questions, consider the following canonical negative feedback control block diagram. Perform Routh Table calculations by hand. For sketching the pole$-$zero maps you may use MATLAB to help factor your polynomial.

$4.[30$pts$]($a$)$ If $G=\frac{(s+3)}{(s-1)(s+2)}$ and $H=\frac{5}{s+5},$ for what range of values for $k,$ if any, does the system become stable in closed$-$loop? Use a Routh Table to justify your answer. $($b$)$ Is this scenario more or less restrictive on the range of $k$ compared to $(3)?($c$)$ What general conclusion would you draw from this example when it comes to adding a left half plane zero to your system's dynamics$-$does it help, or hurt? $($d$)$ Sketch a pole$-$zero map for the case where $k=10.$