Use Descartes' Rule of Signs and the Rational Zeros Theorem $$f ( x ) = 5 x ^ { 3 } - 2 x ^ { 2 } + 25 x - 10$$

question 56

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.
- $$f ( x ) = 5 x ^ { 3 } - 2 x ^ { 2 } + 25 x - 10$$

• A) \(- 5 , - 1 , \frac { 2 } { 5 } ; f ( x ) = ( 5 x - 2 ) ( x + 1 ) ( x + 5 )\)
• B) \(\frac { 2 } { 5 } ; f ( x ) = ( 5 x - 2 ) \left( x ^ { 2 } + 5 \right)\)
• C) \(10 ; f ( x ) = ( x - 10 ) \left( 5 x ^ { 2 } + 1 \right)\)
• D) \(5 , \frac { 2 } { 5 } , 1 ; f ( x ) = ( 5 x - 2 ) ( x - 1 ) ( x - 5 )\)

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