Use the Factor Theorem to Determine Whether X - C $$f ( x ) = 6 x ^ { 3 } + 16 x ^ { 2 } + 18 x - 8 ; c = \frac { 1 } { 3 }$$

question 171

Multiple Choice

Use the Factor Theorem to determine whether x - c is a factor of f. If it is, write f in factored form, that is, write f in the
form f(x) = (x - c) (quotient) .
- $$f ( x ) = 6 x ^ { 3 } + 16 x ^ { 2 } + 18 x - 8 ; c = \frac { 1 } { 3 }$$

• A) Yes; \(f ( x ) = \left\{ x - \frac { 1 } { 3 } \right) \left( 6 x ^ { 2 } + 19 x + 24 \right)\)
• B) Yes; \(f ( x ) = \left( x - \frac { 1 } { 3 } \right) \left( 6 x ^ { 2 } + 18 x + 24 \right)\)
• C) Yes; \(f ( x ) = \left( x + \frac { 1 } { 3 } \right) \left( 6 x ^ { 2 } + 18 x - 24 \right)\)
• D) No

Analyze reasons behind the increasing trend of living alone.

Understand the characteristics and implications of cohabitation.

Identify the challenges and advantages of singlehood in later life.

Explore the role of gender in domestic tasks within cohabiting relationships.

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Definitions:

Fixed Cost

Costs that do not vary with the level of production or sales, such as rent, salaries, and insurance, remaining constant regardless of the amount of goods or services produced.

Demand Curve

A graph showing the relationship between the quantity of a good that consumers are willing and able to purchase and the price of the good.

Marginal Cost

The hike in cost incurred by generating an additional unit of a good or service.

Profit-Maximizing

This is the process by which a firm decides on the price and output level that returns the maximum profit.