Write the Form of the Partial Fraction Decomposition for the Following

question 94

Multiple Choice

Write the form of the partial fraction decomposition for the following rational expression. $\frac { 4 x ^ { 2 } + 3 } { ( x + 8 ) ^ { 3 } }$

• A) \(\frac { A } { x + 8 } + \frac { B } { ( x + 8 ) ^ { 2 } } + \frac { C } { ( x + 8 ) ^ { 3 } }\)
• B) \(\frac { A x ^ { 2 } + C } { ( x + 8 ) ^ { 3 } }\)
• C)\(\frac { A x + B } { x + 8 } + \frac { C x ^ { 2 } + D } { ( x + 8 ) ^ { 2 } } + \frac { E x ^ { 3 } + F } { ( x + 8 ) ^ { 3 } }\)
• D)\(\frac { A } { x + 8 } + \frac { B } { ( x + 8 ) ^ { 3 } }\)
• E)\(\frac { 3 } { x + 8 } + \frac { 4 x ^ { 2 } } { ( x + 8 ) ^ { 2 } } + \frac { A } { ( x + 8 ) ^ { 3 } }\)

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Definitions:

Variables

Elements or factors that can change and affect the outcome of a study or experiment, classified into different types such as independent, dependent, and control variables.

Five-factor Model

A framework identifying five major dimensions of human personality: openness, conscientiousness, extraversion, agreeableness, and neuroticism.

Agreeableness

A personality trait characterized by warmth, kindness, and a willingness to cooperate and avoid conflict.

Neuroticism

A personality trait characterized by moodiness, anxiety, and emotional instability.