$.$ The closed$-$loop transfer function of a system is $[$Section: $6\mathrm{.}3]$

$$

$($

$$

$)$

$=$

$$

$3$

$+$

$2$

$$

$2$

$+$

$7$

$$

$+$

$21$

$$

$5$

$$

$2$

$$

$4$

$+$

$3$

$$

$3$

$$

$6$

$$

$2$

$+$

$2$

$$

$$

$4$

Determine how many closed$-$loop poles lie in the right half$-$plane, in the left half$-$plane, and on the j$-$axis.