Write a Linear Factorization of the Function $$f ( x ) = x ^ { 4 } + 6 x ^ { 3 } + 17 x ^ { 2 } + 54 x + 72$$

question 101

Multiple Choice

Write a linear factorization of the function.
- $$f ( x ) = x ^ { 4 } + 6 x ^ { 3 } + 17 x ^ { 2 } + 54 x + 72$$

• A) \(f ( x ) = ( x + 4 ) ( x + 2 ) \left( x ^ { 2 } + 9 \right)\)
• B) \(f ( x ) = ( x + 4 ) ( x + 2 ) ( x + 3 i ) ( x - 3 i )\)
• C) \(f ( x ) = ( x + 4 ) ( x + 3 ) ( x + 2 i ) ( x - 2 i )\)
• D) \(f ( x ) = ( x + 3 ) ( x + 2 ) ( x + 4 i ) ( x - 4 i )\)

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Definitions:

Resource Demand Curve

A graphical representation showing the relationship between the price of a resource and the quantity of that resource that firms are willing to employ, holding all other factors constant.

Competitive Market

A market structure characterized by many buyers and sellers where no single entity has the power to significantly affect the prices of goods and services.

Product Demand Elasticity

A measure of how sensitive the quantity demanded of a product is to changes in its price.

Marginal Productivity Theory

An economic theory that explains how the value of a productive input is determined by its contribution to the total output.