For the Polynomial, List Each Real Zero and Its Multiplicity $$f ( x ) = 2 \left( x ^ { 2 } + 1 \right) \left( x ^ { 2 } + 6 \right) ^ { 2 }$$

question 34

Multiple Choice

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at
each x -intercept.
- $$f ( x ) = 2 \left( x ^ { 2 } + 1 \right) \left( x ^ { 2 } + 6 \right) ^ { 2 }$$

• A) No real zeros
• B) \(- 1\), multiplicity 1 , touches \(x\)-axis; \(- 6\), multiplicity 2 , crosses \(x\)-axis
• C) 1 , multiplicity 1 , crosses \(x\)-axis; \(- 1\), multiplicity 1 , crosses \(x\)-axis; \(\sqrt { 6 }\), multiplicity 2 , touches \(x\)-axis; \(- \sqrt { 6 }\), multiplicity 2 , touches \(x\)-axis
• D) \(- 1\), multiplicity 1 , crosses \(x\)-axis; \(- 6\), multiplicity 2 , touches \(x\)-axis

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Definitions:

Increasing-Cost Industry

An industry in which expansion through the entry of new firms raises the prices firms in the industry must pay for resources and therefore increases their production costs.

Economic Losses

Losses incurred when a company or economy's total costs exceed its total revenues, indicating a negative profit situation.

Industry Supply

The total quantity of a good or service that all producers in an industry are willing and able to sell at various prices over a certain period.

Marginal Cost

The elevation in overall cost triggered by assembling an extra unit of a product or service.