Write the Polynomial in Completely Factored Form $x ^ { 2 } + 1 .$

Multiple Choice

Write the polynomial in completely factored form. (Hint: One factor is $x ^ { 2 } + 1 .$ )
$$f ( x ) = x ^ { 4 } + 6 x ^ { 3 } + 14 x ^ { 2 } + 6 x + 13$$

A) $f ( x ) = ( x - 2 ) ( x + 2 ) ( x + 3 - i ) ( x + 3 + i )$
B) $f ( x ) = ( x - 3 ) ( x + 3 ) ( x - 1 - 2 i ) ( x - 1 + 2 i )$
C) $f ( x ) = ( x - 1 ) ( x + 1 ) ( x + 3 - 2 i ) ( x + 3 + 2 i )$
D) $f ( x ) = ( x - 3 i ) ( x + 3 i ) ( x - 1 - 2 i ) ( x - 1 + 2 i )$
E) $f ( x ) = ( x - i ) ( x + i ) ( x + 3 - 2 i ) ( x + 3 + 2 i )$