Find All Zeros of the Function and Write the Polynomial $$f ( x ) = x ^ { 3 } - x ^ { 2 } + 16 x - 16$$

question 12

Multiple Choice

Find all zeros of the function and write the polynomial as a product of linear factors.
- $$f ( x ) = x ^ { 3 } - x ^ { 2 } + 16 x - 16$$

• A) \(f ( x ) = ( x - 1 ) ( x + 4 i ) ( x - 4 i )\)
• B) \(f ( x ) = ( x - 1 ) ( x + 1 ) ( x + 16 )\)
• C) \(f ( x ) = ( x - 25 ) ( x + i ) ( x - i )\)
• D) \(f ( x ) = ( x - 1 ) ( x + 4 ) ( x - 4 )\)

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Definitions:

Constant-cost Industry

An industry where the costs of production do not change as the total output in the industry changes.

Long-run Supply

Long-run Supply refers to the quantity of a good that producers are willing and able to supply onto the market at different price levels when all production inputs can be varied.

Supply Curve

A graph showing the relationship between the price of a good and the quantity of that good that producers are willing to supply.

Increasing-cost Industry

An industry in which the costs of production increase as the industry expands due to factors like limited resources or higher input prices.