Given that when polynomial $f ( x )$ is divided by $x ^ { 2 } + 5 x + 1$, the quotient is $x ^ { 3 } + 7 x ^ { 2 } + x + 3$, select the options that could be $f ( x )$.
(1) $2 \left( x ^ { 3 } + 7 x ^ { 2 } + x + 3 \right) \left( x ^ { 2 } + 5 x + 1 \right)$
(2) $\left( x ^ { 3 } + 7 x ^ { 2 } + x + 3 \right) \left( x ^ { 2 } + 5 x + 1 \right) - x$
(3) $\left( x ^ { 3 } + 7 x ^ { 2 } + x + 3 \right) \left( x ^ { 2 } + 5 x + 1 \right) + x ^ { 2 }$
(4) $\left( x ^ { 3 } + 7 x ^ { 2 } + x + 4 \right) \left( x ^ { 2 } + 5 x + 1 \right) - x$
(5) $\left( x ^ { 3 } + 7 x ^ { 2 } + x + 4 \right) \left( x ^ { 2 } + 5 x + 1 \right) - x ^ { 2 }$

A real-coefficient cubic polynomial $f ( x )$ divided by $x + 6$ gives quotient $q ( x )$ and remainder 3. If $q ( x )$ has a maximum value of 8 at $x = - 6$, then the coordinates of the center of symmetry of the graph $y = f ( x )$ are ((13-1) (13-2), (13-3)).