Find the Partial Fraction Decomposition for the Rational Expression $\frac { 2 x ^ { 3 } - 3 x ^ { 2 } - 2 x + 27 } { x ^ { 2 } + x - 2 }$

question 385

Multiple Choice

Find the partial fraction decomposition for the rational expression.
$\frac { 2 x ^ { 3 } - 3 x ^ { 2 } - 2 x + 27 } { x ^ { 2 } + x - 2 }$

• A) \(2 x - 9 + \frac { - 5 / 3 } { x + 2 } + \frac { 1 / 3 } { x - 1 }\)
• B) \(2 x - 5 + \frac { - 7 / 3 } { x + 2 } + \frac { 13 / 3 } { x - 1 }\)
• C) \(2 x - 9 + \frac { - 13 } { x + 2 } + \frac { 7 } { x - 1 }\)
• D) \(2 x - 5 + \frac { - 1 } { x + 2 } + \frac { 8 } { x - 1 }\)

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Definitions:

Perceptual Tendency

The inclination to perceive information, situations, or objects in a specific way based on past experiences and personal biases.

Fundamental Attribution Error

The tendency to overestimate the influence of personality and underestimate the impact of situational factors in explaining someone else's behavior.

Projection

A defense mechanism where an individual attributes their own unacceptable thoughts or feelings onto someone else.

Consensus Cue

A signal or piece of information indicating that a group is reaching or has reached general agreement on a particular issue.