Use Long Division to Divide the First Polynomial Below by the Second

question 3

Multiple Choice

Use long division to divide the first polynomial below by the second. $x ^ { 5 } + x ^ { 4 } + 7 x ^ { 3 } + x ^ { 2 } + 6 x - 27,$ $x ^ { 2 } + 6$

• A) \(x ^ { 3 } + x ^ { 2 } - 5 x + 3 + \frac { 1 } { x ^ { 2 } + 6 }\)
• B) \(x ^ { 3 } + x ^ { 2 } + x - 5 + \frac { 3 } { x ^ { 2 } + 6 }\)
• C) \(x ^ { 3 } + x ^ { 2 } + x + 3 + \frac { 1 } { x ^ { 2 } + 6 }\)
• D) \(x ^ { 3 } + 3 x ^ { 2 } + x + 1 - \frac { 5 } { x ^ { 2 } + 6 }\)
• E) \(x ^ { 3 } - 5 x ^ { 2 } + 3 x + 1 + \frac { 1 } { x ^ { 2 } + 6 }\)

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Definitions:

Process Addiction

A behavioral addiction where an individual becomes compulsively engaged in an activity that does not involve an addictive substance, such as gambling, eating, or shopping.

PHQ-2

A brief, initial screening tool consisting of two questions used to assess the presence of depressive symptoms.

Depressive Disorder

A mental health disorder characterised by persistently depressed mood or loss of interest in activities, causing significant impairment in daily life.

Detection Window

The period during which a particular substance or marker can be identified or detected through testing.