For a polynomial function $f ( x )$, define the function $g ( x )$ as
$$g ( x ) = x ^ { 2 } f ( x )$$
If $f ( 2 ) = 1$ and $f ^ { \prime } ( 2 ) = 3$, what is the value of $g ^ { \prime } ( 2 )$? [3 points]\\
(1) 12\\
(2) 14\\
(3) 16\\
(4) 18\\
(5) 20