Write the Polynomial as the Product of Factors That Are $\left( x ^ { 2 } + 9 \right) \left( x ^ { 4 } - 3 \right)$

question 38

Multiple Choice

Write the polynomial as the product of factors that are irreducible over the rationals. ?
F(x) = x⁴ + 6x² - 27
?

• A) \(\left( x ^ { 2 } + 9 \right) \left( x ^ { 4 } - 3 \right)\)
• B) \(\left( x ^ { 2 } + 9 \right) \left( x ^ { 2 } - 3 \right)\)
• C) \(( x + 9 ) \left( x ^ { 2 } - 3 \right)\)
• D) \(( x + 6 ) \left( x ^ { 2 } - 3 \right)\)
• E) \(\left( x ^ { 2 } + 9 \right) ( x + \sqrt { 3 } ) ( x + \sqrt { 3 } )\)

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Definitions:

Positive Reinforcement

The process of encouraging or establishing a pattern of behavior by offering reward when that behavior is exhibited.

Negative Reinforcement

A process in behavioral psychology where the removal of an unfavorable event or outcome after the display of a behavior increases the likelihood of the behavior being repeated in the future.

Positive Punishment

Adding an unfavorable outcome or event following an undesired behavior to decrease the likelihood of that behavior happening in the future.

Negative Punishment

The removal of a desirable stimulus following a behavior, intended to decrease the likelihood of that behavior occurring again.