Use Descartes' Rule of Signs and the Rational Zeros Theorem $$f ( x ) = x ^ { 4 } - 15 x ^ { 2 } - 16$$

question 63

Multiple Choice

Use Descartes' Rule of Signs and the Rational Zeros Theorem to find all the real zeros of the polynomial function. Use the
zeros to factor f over the real numbers.
- $$f ( x ) = x ^ { 4 } - 15 x ^ { 2 } - 16$$

• A) \(- 4,4 ; f ( x ) = ( x - 4 ) ( x + 4 ) \left( x ^ { 2 } + 1 \right)\)
• B) \(4 ; f ( x ) = ( x - 4 ) ^ { 2 } \left( x ^ { 2 } + 1 \right)\)
• C) \(- 1,1 ; f ( x ) = ( x - 1 ) ( x + 1 ) \left( x ^ { 2 } + 16 \right)\)
• D) \(- 4 , - 1,4,1 ; f ( x ) = ( x - 4 ) ( x + 4 ) ( x - 1 ) ( x + 1 )\)

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