Factor the Denominator of the Given Rational Expression, and Then $\frac { 1 } { x ^ { 3 } + x ^ { 2 } - 44 x + 96 }$

question 16

Multiple Choice

Factor the denominator of the given rational expression, and then find the partial fraction decomposition. $\frac { 1 } { x ^ { 3 } + x ^ { 2 } - 44 x + 96 }$

• A) \(\frac { \frac { 1 } { 11 } } { x - 3 } + \frac { - \frac { 1 } { 12 } } { x - 4 } + \frac { \frac { 1 } { 132 } } { x + 8 }\)
• B) \(\frac { - \frac { 1 } { 11 } } { x - 3 } + \frac { - \frac { 1 } { 12 } } { x - 4 } + \frac { \frac { 1 } { 132 } } { x + 8 }\)
• C) \(\frac { \frac { 1 } { 11 } } { x - 3 } + \frac { - \frac { 1 } { 12 } } { x - 4 } + \frac { - \frac { 1 } { 132 } } { x + 8 }\)
• D) \(\frac { - \frac { 1 } { 11 } } { x - 3 } + \frac { \frac { 1 } { 12 } } { x - 4 } + \frac { \frac { 1 } { 132 } } { x + 8 }\)
• E) \(\frac { - \frac { 1 } { 11 } } { x - 3 } + \frac { \frac { 1 } { 12 } } { x - 4 } + \frac { - \frac { 1 } { 132 } } { x + 8 }\)

---

Definitions:

Borderline

A term often used to describe a condition, situation, or quality that is indeterminately between two states or classifications, especially in psychology where it refers to Borderline Personality Disorder.

Narcissistic

Pertaining to narcissism, characterized by an excessive preoccupation with oneself and one's physical appearance, abilities, and needs.

Antisocial

Behaviors or attitudes that go against the norms of society, often harming others or violating social rules.

Self-Destructive Acts

Behaviors or actions undertaken by an individual, which cause harm or damage to themselves, often as a way of coping with distress or emotional pain.