Find the Partial Fraction Decomposition for the Rational Expression $$\frac { 4 x ^ { 3 } + 8 x ^ { 2 } + 5 x - 7 } { 2 x ^ { 2 } - x - 1 }$$

question 413

Multiple Choice

Find the partial fraction decomposition for the rational expression.
- $$\frac { 4 x ^ { 3 } + 8 x ^ { 2 } + 5 x - 7 } { 2 x ^ { 2 } - x - 1 }$$

• A) \(2 x - 5 + \frac { - 5 } { 6 x + 3 } + \frac { 1 } { 3 x - 3 }\)
• B) \(2 x + 5 + \frac { 16 } { 6 x + 3 } + \frac { 10 } { 3 x - 3 }\)
• C) \(2 x - 5 + \frac { 13 } { 2 x + 1 } + \frac { 7 } { x - 1 }\)
• D) \(2 x + 5 + \frac { - 7 } { 6 x + 3 } + \frac { 13 } { 3 x - 3 }\)

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Definitions:

Self-fulfilling Prophecy

A prediction that directly or indirectly causes itself to become true, due to positive feedback between belief and behavior.

Stereotype Threat

The risk of confirming negative stereotypes about an individual's racial, ethnic, gender, or cultural group that can hinder performance in relevant areas.

Social Comparison

A theory positing that individuals determine their own social and personal worth based on how they stack up against others they perceive as somehow faring better or worse.

Attribution Theory

A theory focused on how people interpret and understand their experiences by ascribing causes to behaviors and events.