An LTI system has the transfer function

H$($z$)=($z$1)($z$6)($z$2)($z$3).$H$($z$)=\backslash$frac$\{($z $-1)($z $-6)\}\{($z $-2)($z $-3)\}.$H$($z$)=($z$2)($z$3)($z$1)($z$6).$

Compute the following:

$($a$)$ The zeros and poles. Is the system stable?

$($b$)$ The difference equation.

$($c$)$ The response to input x$[$n$]=\{1,5,6\}$x$[$n$]=\backslash \{1,-5,6\backslash \}$x$[$n$]=\{1,5,6\}.$

$($d$)$ The impulse response h$[$n$]$h$[$n$]$h$[$n$].$