Use Descartes' Rule of Signs and the Rational Zeros Theorem $$f ( x ) = 5 x ^ { 4 } - 8 x ^ { 3 } + 23 x ^ { 2 } - 32 x + 12$$

question 31

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.
- $$f ( x ) = 5 x ^ { 4 } - 8 x ^ { 3 } + 23 x ^ { 2 } - 32 x + 12$$

• A) \(- 4 , - 1,1 , \frac { 3 } { 5 } ; f ( x ) = ( x - 1 ) ( 5 x - 3 ) ( x + 1 ) ( x + 4 )\)
• B) \(1 , \frac { 3 } { 5 } ; f ( x ) = ( x - 1 ) ( 5 x - 3 ) \left( x ^ { 2 } + 4 \right)\)
• C)\(4 , \frac { 3 } { 5 } ; f ( x ) = ( x - 4 ) ( 5 x - 3 ) \left( x ^ { 2 } + 1 \right)\)
• D) \(- 4 , - 1,1 , - \frac { 3 } { 5 } ; f ( x ) = ( x - 1 ) ( 5 x + 3 ) ( x + 1 ) ( x + 4 )\)

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