Use Descartes' Rule of Signs and the Rational Zeros Theorem $$f ( x ) = 4 x ^ { 4 } - 8 x ^ { 3 } + 5 x ^ { 2 } - 2 x + 1$$

question 114

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.
- $$f ( x ) = 4 x ^ { 4 } - 8 x ^ { 3 } + 5 x ^ { 2 } - 2 x + 1$$

• A) \(- 1,1 ; f ( x ) = ( x - 1 ) ( x + 1 ) \left( 4 x ^ { 2 } + 1 \right)\)
• B) no real roots; \(\mathrm { f } ( \mathrm { x } ) = \left( \mathrm { x } ^ { 2 } + 1 \right) \left( 4 \mathrm { x } ^ { 2 } + 1 \right)\)
• C) \(- 1\), multiplicity 2; \(f ( x ) = ( x + 1 ) ^ { 2 } \left( 4 x ^ { 2 } + 1 \right)\)
• D) 1 , multiplicity 2; \(\mathrm { f } ( \mathrm { x } ) = ( \mathrm { x } - 1 ) ^ { 2 } \left( 4 \mathrm { x } ^ { 2 } + 1 \right)\)

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