Find All Rational Zeros and Factor F(x) $f ( x ) = 6 x ^ { 3 } + 19 x ^ { 2 } + 8 x - 5$

question 69

Multiple Choice

Find all rational zeros and factor f(x) .
$f ( x ) = 6 x ^ { 3 } + 19 x ^ { 2 } + 8 x - 5$

• A) \(1 , - \frac { 5 } { 2 } , - \frac { 1 } { 3 } ; f ( x ) = ( x - 1 ) ( 3 x + 1 ) ( 2 x + 5 )\)
• B) \(1 , - 5 , - \frac { 1 } { 6 } ; f ( x ) = ( x - 1 ) ( 6 x + 1 ) ( x + 5 )\)
• C) \(- 1 , - 5 , \frac { 1 } { 6 } ; f ( x ) = ( x + 1 ) ( 6 x - 1 ) ( x + 5 )\)
• D) \(- 1 , - \frac { 5 } { 2 } , \frac { 1 } { 3 } ; f ( x ) = ( x + 1 ) ( 3 x - 1 ) ( 2 x + 5 )\)

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Definitions:

Chloromethane

A colorless, flammable gas with a mild sweet odor, used in manufacturing and as a refrigerant; its chemical formula is CH3Cl.

Monochlorination

The chemical process of introducing one chlorine atom into a molecule, commonly used in the organic synthesis of chlorinated compounds.

Methane

A simple hydrocarbon with the chemical formula CH4, known as the simplest alkane and a primary component of natural gas.

Presence

The existence or occurrence of a particular substance or entity within a specific environment or context.