Decompose P/Q, Where Q Has a Prime, Repeated Quadratic Factor $$\frac { 3 x - 1 } { \left( x ^ { 2 } + x + 1 \right) ^ { 2 } }$$

question 269

Multiple Choice

Decompose P/Q, Where Q Has a Prime, Repeated Quadratic Factor
Write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the
constants.
- $$\frac { 3 x - 1 } { \left( x ^ { 2 } + x + 1 \right) ^ { 2 } }$$

• A) \(\frac { A x + B } { x ^ { 2 } + x + 1 } + \frac { C x + D } { \left( x ^ { 2 } + x + 1 \right) ^ { 2 } }\)
• B) \(\frac { \mathrm { A } } { \mathrm { x } ^ { 2 } + \mathrm { x } + 1 } + \frac { \mathrm { Bx } + \mathrm { C } } { \left( \mathrm { x } ^ { 2 } + \mathrm { x } + 1 \right) ^ { 2 } }\)
• C) \(\frac { \mathrm { A } } { \mathrm { x } ^ { 2 } + \mathrm { x } + 1 } + \frac { \mathrm { B } } { \left( \mathrm { x } ^ { 2 } + \mathrm { x } + 1 \right) ^ { 2 } }\)
• D) \(\frac { A x + B } { x ^ { 2 } + x + 1 } + \frac { C } { \left( x ^ { 2 } + x + 1 \right) ^ { 2 } }\)

---

Definitions:

Gender Differences

The distinctions in characteristics, behavior, and roles typically associated with being male or female.

Activity Levels

Activity Levels describe the amount of physical or mental exertion that a person engages in during daily life.

5-7 Shift

A developmental stage where children start to use thought processes to experience their world, showing logical, though not yet abstract, reasoning.

Intelligence Scores

Quantitative measures obtained from intelligence tests that aim to represent an individual's cognitive abilities relative to a statistical norm.