Decompose P/Q, Where Q Has a Prime, Repeated Quadratic Factor $$\frac { 7 x + 2 } { ( x - 4 ) \left( x ^ { 2 } + x + 2 \right) ^ { 2 } }$$

question 248

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.
- $$\frac { 7 x + 2 } { ( x - 4 ) \left( x ^ { 2 } + x + 2 \right) ^ { 2 } }$$

• A) \(\frac { A } { x - 4 } + \frac { B x + C } { x ^ { 2 } + x + 2 } + \frac { D x + E } { \left( x ^ { 2 } + x + 2 \right) ^ { 2 } }\)
• B) \(\frac { A } { x - 4 } + \frac { B } { x ^ { 2 } + x + 2 } + \frac { C } { \left( x ^ { 2 } + x + 2 \right) ^ { 2 } }\)
• C) \(\frac { \mathrm { A } } { \mathrm { x } - 4 } + \frac { \mathrm { B } } { \mathrm { x } ^ { 2 } + \mathrm { x } + 2 } + \frac { \mathrm { Cx } + \mathrm { D } } { \left( \mathrm { x } ^ { 2 } + \mathrm { x } + 2 \right) ^ { 2 } }\)
• D) \(\frac { A } { x - 4 } + \frac { B x + C } { x ^ { 2 } + x + 2 }\) Write the partial fraction decomposition of the rational expression.

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Definitions:

Operant Conditioning

An educational method where behavior is altered by the application of rewards or penalties.

Reinforced

In behavioral psychology, refers to any stimulus which strengthens or increases the probability of a specific response.

Behavior

The range of actions and observable emotions of individuals or groups in response to external or internal stimuli.

Continuous Reinforcement

A learning schedule in which a behavior is reinforced each time it occurs, leading to a rapid acquisition of the behavior.