Write $f ( x ) = x ^ { 4 } - 12 x ^ { 3 } + 59 x ^ { 2 } - 138 x + 130$

question 89

Multiple Choice

Write $f ( x ) = x ^ { 4 } - 12 x ^ { 3 } + 59 x ^ { 2 } - 138 x + 130$ as a product of linear factors.

• A) \(( x - 3 - i ) ( x - 3 + 2 i ) ( x - 3 - 2 i ) ( x - 2 + i )\)
• B) \(( x - 3 - i ) ( x - 3 + i ) ( x - 2 - i ) ( x - 2 + i )\)
• C) \(( x - 3 - i ) ( x - 3 + i ) ( x + 3 - 2 i ) ( x - 2 + i )\)
• D) \(( x - 3 + i ) ( x - 3 - i ) ( x - 2 + 3 i ) ( x - 2 - 3 i )\)
• E) \(( x - 3 + i ) ( x - 3 - i ) ( x - 3 + 2 i ) ( x - 3 - 2 i )\)

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Definitions:

Finite Population

A set of data or a population that is limited or fixed in size, often used in statistical analysis to apply different formulae compared to an infinite population.

Average Service Time

The mean duration needed to complete service for a customer or process a task, commonly used in the evaluation of service and operational efficiency.

Service Factor

A multiplier used in engineering and operations management to account for potential variability in demand or capacity, ensuring systems can handle peak loads.