Write $f ( x ) = x ^ { 3 } + 3 x ^ { 2 } + 16 x + 48$

question 27

Multiple Choice

Write $f ( x ) = x ^ { 3 } + 3 x ^ { 2 } + 16 x + 48$ as a product of linear factors.

• A) \(x = ( x - 3 ) ^ { 2 } ( x - 4 i )\)
• B) \(x = ( x - 3 ) ( x - 4 ) ^ { 2 }\)
• C) \(x = ( x + 3 ) ( x - 3 ) ( x + 4 )\)
• D) \(x = ( x + 3 ) ( x + 4 i ) ( x - 4 i )\)
• E) \(x = ( x - 3 ) ( x + 4 ) ^ { 2 }\)

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Definitions:

One Controller

In control systems, having one controller implies a system design where a single controller unit manages the operations of multiple processes or devices.

Feedback Element

A component in a control system that provides real-time input based on the output, helping to adjust the system's behavior.

Deadband

A range within which an input signal can vary without initiating a response or change in the output, used to prevent frequent or unnecessary adjustments.