Use Descartes' Rule of Signs and the Rational Zeros Theorem $$f ( x ) = 3 x ^ { 3 } - 2 x ^ { 2 } + 9 x - 6$$

question 34

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.
- $$f ( x ) = 3 x ^ { 3 } - 2 x ^ { 2 } + 9 x - 6$$

• A) \(6 ; f ( x ) = ( x - 6 ) \left( 3 x ^ { 2 } + 1 \right)\)
• B) \(3 , \frac { 2 } { 3 } , 1 ; f ( x ) = ( 3 x - 2 ) ( x - 1 ) ( x - 3 )\)
• C) \(\frac { 2 } { 3 } ; f ( x ) = ( 3 x - 2 ) \left( x ^ { 2 } + 3 \right)\)
• D) \(- 3 , - 1 , \frac { 2 } { 3 } ; f ( x ) = ( 3 x - 2 ) ( x + 1 ) ( x + 3 )\)

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