Write the Polynomial $x ^ { 4 } - 5 x ^ { 3 } + 4 x ^ { 2 } + x - 15$

question 101

Multiple Choice

Write the polynomial $x ^ { 4 } - 5 x ^ { 3 } + 4 x ^ { 2 } + x - 15$ in completely factored form. (Hint: One factor is $x ^ { 2 } - 2 x + 3$ .)

• A) \(( x - 1 + \sqrt { 2 } i ) ( x + 1 + \sqrt { 2 } i ) \left( x - \frac { 3 + \sqrt { 29 } } { 2 } \right) \left( x - \frac { 3 - \sqrt { 29 } } { 2 } \right)\)
• B) \(( x - 1 + \sqrt { 2 } i ) ( x + 1 - \sqrt { 2 } i ) \left( x - \frac { 3 + \sqrt { 29 } } { 2 } \right) \left( x - \frac { 3 - \sqrt { 29 } } { 2 } \right)\)
• C) \(( x - 1 + \sqrt { 2 } i ) ( x - 1 + \sqrt { 2 } i ) \left( x - \frac { 3 + \sqrt { 29 } } { 2 } \right) \left( x - \frac { 3 - \sqrt { 29 } } { 2 } \right)\)
• D) \(( x + 1 + \sqrt { 2 i } ) ( x - 1 + \sqrt { 2 i } ) \left( x - \frac { 3 + \sqrt { 29 } } { 2 } \right) \left( x - \frac { 3 - \sqrt { 29 } } { 2 } \right)\)
• E) \(( x - 1 + \sqrt { 2 } i ) ( x - 1 - \sqrt { 2 } i ) \left( x - \frac { 3 + \sqrt { 29 } } { 2 } \right) \left( x - \frac { 3 - \sqrt { 29 } } { 2 } \right)\)

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