If $x = 4$ Is a Root Of $x ^ { 3 } + 5 x ^ { 2 } - 16 x - 80 = 0$

question 65

Multiple Choice

If $x = 4$ is a root of $x ^ { 3 } + 5 x ^ { 2 } - 16 x - 80 = 0$ , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

• A) \(( x - 5 ) ( x - 4 ) ( x + 4 ) ; x = 5,4 , - 4\)
• B) \(( x + 5 ) ( x - 4 ) ( x + 4 ) ; x = - 5,4 , - 4\)
• C) \(( x + 5 ) ( x - 4 ) ^ { 2 } ; x = - 5,4\)
• D) \(( x + 5 ) ^ { 2 } ( x - 4 ) ; x = - 5,4\)
• E) \(( x + 5 ) ( x - 5 ) ( x + 4 ) ; x = - 5,5 , - 4\)

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Definitions:

Risk Neutral

An attitude or preference indicating indifference between choices with uncertain outcomes, focusing instead on the expected values.

Risk Averse

A characteristic of preferring to avoid risk, inclining towards guaranteed outcomes over potentially higher-yielding but uncertain ones.

Income

The accumulation of funds, characteristically on a habitual basis, through work or investing.

Von Neumann-Morgenstern

A theory of expected utility that describes how rational individuals choose among uncertain prospects, emphasizing the maximization of utility for decision-making under uncertainty.