If $x = \sqrt { 6 }$ Is a Root Of $x ^ { 3 } + 5 x ^ { 2 } - 6 x - 30 = 0$

question 38

Multiple Choice

If $x = \sqrt { 6 }$ is a root of $x ^ { 3 } + 5 x ^ { 2 } - 6 x - 30 = 0$ , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

• A) \(( x + 5 ) ( x - \sqrt { 6 } ) ( x + \sqrt { 6 } ) ; - 5 , \sqrt { 6 } , - \sqrt { 6 }\)
• B) \(( x - 5 ) ( x + \sqrt { 6 } ) ^ { 2 } ; 5 , \sqrt { 6 }\)
• C) \(( x - 5 ) ( x - \sqrt { 6 } ) ^ { 2 } ; 5 , \sqrt { 6 }\)
• D) \(( x - 5 ) ( x + \sqrt { 6 } ) ^ { 2 } ; - 5 , - \sqrt { 6 }\)
• E) \(( x - 5 ) ^ { 2 } ( x - \sqrt { 6 } ) ^ { 2 } ; 5 , \sqrt { 6 }\)

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Definitions:

Piaget

Jean Piaget was a Swiss psychologist known for his work on child development and cognitive development theory.

Moral Judgments

Evaluations or decisions about the rightness or wrongness of actions, often guided by societal norms and personal values.

Psychological Reasoning

Psychological reasoning involves the process of using logical, rational thinking and mental activities to understand human behavior and cognitive processes.

Moral Intuitions

Immediate, gut-level feelings that guide judgments of right and wrong without conscious reasoning.