Decompose P/Q, Where Q Has a Nonrepeated Prime Quadratic Factor $$\frac { 5 x ^ { 2 } + 7 x + 11 } { x ^ { 3 } + 4 x ^ { 2 } + 5 x + 20 }$$

question 48

Multiple Choice

Decompose P/Q, Where Q Has a Nonrepeated Prime Quadratic Factor
Write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the
constants.
- $$\frac { 5 x ^ { 2 } + 7 x + 11 } { x ^ { 3 } + 4 x ^ { 2 } + 5 x + 20 }$$

• A) \(\frac { 3 } { x + 4 } + \frac { 2 x - 1 } { x ^ { 2 } + 5 }\)
• B) \(\frac { 3 } { x + 4 } + \frac { 2 } { x ^ { 2 } + 5 }\)
• C) \(\frac { 3 } { x + 5 } + \frac { 2 x - 1 } { x ^ { 2 } + 4 }\)
• D) \(\frac { 3 } { x + 4 } + \frac { 2 } { x + 5 } + \frac { - 1 } { ( x + 5 ) ^ { 2 } }\)

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Definitions:

Conflict

A situation where competing or opposing needs, interests, or viewpoints lead to disagreement or dispute.

Negatively Affected

Impacted in an adverse manner, leading to detrimental outcomes or decreases in quality, performance, or well-being.

Intrapersonal Conflict

A psychological struggle within oneself that arises from opposing interests, beliefs, or needs.

Realistic Alternative

A feasible and practical option that can be considered when making decisions or solving problems.