Write the Partial Fraction Decomposition of the Improper Rational Expression $$\frac { x ^ { 3 } - 4 x ^ { 2 } + 3 x + 2 } { x ^ { 2 } + x - 2 }$$

question 78

Multiple Choice

Write the partial fraction decomposition of the improper rational expression.
$$\frac { x ^ { 3 } - 4 x ^ { 2 } + 3 x + 2 } { x ^ { 2 } + x - 2 }$$

• A) \(x - 5 + \frac { 1 } { 3 } \left( \frac { 2 } { x - 1 } + \frac { 28 } { x + 2 } \right)\)
• B) \(x - 5 + \frac { 1 } { 3 } \left( \frac { 18 } { x - 1 } + \frac { 28 } { x + 2 } \right)\)
• C) \(x - 5 + \frac { 1 } { 3 } \left( \frac { 18 } { x + 1 } + \frac { 28 } { x - 2 } \right)\)
• D) \(x - 5 + \frac { 1 } { 3 } \left( \frac { 2 } { x - 1 } - \frac { 28 } { x + 2 } \right)\)
• E) \(\frac { 1 } { 3 } \left( \frac { 2 } { x - 1 } + \frac { 28 } { x + 2 } \right)\)

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Definitions:

Intuitive Thought

The process of knowing or understanding something instinctively, without the need for conscious reasoning.

Concrete Operational

A stage in Piaget’s theory of cognitive development (roughly ages 7 to 11) during which children gain the ability to think logically about concrete events.

Analytic

Pertaining to or resulting from the process of breaking down complex information or problems into simpler parts for better understanding or resolution.

Abstract

Pertaining to ideas, concepts, or qualities not associated with specific objects or events and not having physical existence.