Solve the Problem $$f ( x ) = x ^ { 4 } - 4 x ^ { 2 } - 221$$

Solve the problem.
- $$f ( x ) = x ^ { 4 } - 4 x ^ { 2 } - 221$$
a. Factor the polynomial over the set of real numbers.
b. Factor the polynomial over the set of complex numbers.

A) a. $f ( x ) = ( x - \sqrt { 13 } ) ( x + \sqrt { 13 } ) \left( x ^ { 2 } + 17 \right)$
b. $f ( x ) = ( x - \sqrt { 13 } ) ( x + \sqrt { 13 } ) ( x + \sqrt { 17 } i ) ( x - \sqrt { 17 } i )$

B) a. $f ( x ) = \left( x - \sqrt { 17 } \left( x + \sqrt { 17 } \left( x ^ { 2 } + 13 \right) \right. \right.$
b. $f ( x ) = ( x - \sqrt { 17 } ) ( x + \sqrt { 17 } ) ( x + \sqrt { 13 } i ) ( x - \sqrt { 13 } i )$

C) a. $f ( x ) = ( x - \sqrt { 17 } ) ( x + \sqrt { 17 } ) ( x - \sqrt { 13 } ) ( x + \sqrt { 13 } )$
b. $f ( x ) = ( x - \sqrt { 17 } ) ( x + \sqrt { 17 } ) ( x + \sqrt { 13 } ) ( x - \sqrt { 13 } )$

D) a. $f ( x ) = \left( x ^ { 2 } + 17 \right) \left( x ^ { 2 } + 13 \right)$
b. $f ( x ) = ( x - \sqrt { 17 } i ) ( x + \sqrt { 17 } i ) ( x + \sqrt { 13 } i ) ( x - \sqrt { 13 } i )$