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

question 147

Multiple Choice

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. \(f ( x ) = ( x - \sqrt { 17 } i ) ( x + \sqrt { 17 } i ) ( x + \sqrt { 13 } i ) ( x - \sqrt { 13 } i )\)

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