Factor the Denominator of the Given Rational Expression, and Then $\frac { 2 x ^ { 3 } + 11 x - 3 } { x ^ { 4 } + 6 x ^ { 2 } + 9 }$

question 11

Multiple Choice

Factor the denominator of the given rational expression, and then find the partial fraction decomposition. $\frac { 2 x ^ { 3 } + 11 x - 3 } { x ^ { 4 } + 6 x ^ { 2 } + 9 }$

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

---

Definitions:

Worker Adjustment and Retraining Notification Act

A U.S. federal law that requires employers to provide advance notice in cases of qualifying plant closings and mass layoffs.

McDonnell-Douglas Test

The McDonnell-Douglas test is used as the basis for establishing a prima facie case of disparate impact discrimination.

Prima Facie Case

An established case at first glance, where the evidence before trial is sufficient to prove the case unless there is substantial contradictory evidence presented.

Americans with Disabilities Act

A law focused on civil rights that forbids any form of discrimination towards people with disabilities, covering every public aspect such as employment, education, transportation, and both public and private spaces accessible to the public.