Find the Partial Fraction Decomposition for the Rational Expression $$\frac { 4 x ^ { 3 } + 8 x ^ { 2 } - 6 x + 2 } { 2 x ^ { 2 } - x - 1 }$$

question 232

Multiple Choice

Find the partial fraction decomposition for the rational expression.
- $$\frac { 4 x ^ { 3 } + 8 x ^ { 2 } - 6 x + 2 } { 2 x ^ { 2 } - x - 1 }$$

• A) \(2 x + 5 + \frac { - 7 } { 6 x + 3 } + \frac { 13 } { 3 x - 3 }\)
• B) \(2 x + 5 + \frac { - 13 } { 6 x + 3 } + \frac { 8 } { 3 x - 3 }\)
• C) \(2 x - 5 + \frac { - 13 } { 2 x + 1 } + \frac { 7 } { x - 1 }\)
• D) \(2 x - 5 + \frac { - 5 } { 6 x + 3 } + \frac { 1 } { 3 x - 3 }\)

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Definitions:

Perceived Control

The belief or perception that one can influence the events in their life, which has significant effects on psychological well-being.

Framing Effect

A cognitive bias where people react differently based on the way information is presented to them, particularly in decisio-making scenarios.

Category Hierarchies

Organizational systems that classify groups or objects into ranked categories based on shared characteristics or importance.

Representativeness Heuristic

A cognitive shortcut where the likelihood of an object belonging to a category is assessed based on how typical the object seems of the category.