Write the Function in the Form F(x) = (X - $f ( x ) = x ^ { 3 } - 1 x ^ { 2 } - 14 x + 12 \quad k = 4$

question 70

Multiple Choice

Write the function in the form f(x) = (x - k) q(x) + r for the given value of k and demonstrate that f(k) = r. $f ( x ) = x ^ { 3 } - 1 x ^ { 2 } - 14 x + 12 \quad k = 4$

• A) \(( x - 4 ) \left( x ^ { 2 } - 3 x - 2 \right) + 4\)
• B) \(( x + 4 ) \left( x ^ { 2 } + 3 x - 2 \right) + 4\)
• C) \(( x - 4 ) \left( x ^ { 2 } + 3 x - 2 \right) + 4\)
• D) \(( x - 4 ) \left( x ^ { 2 } + 3 x - 2 \right) - 4\)
• E) \(( x - 4 ) \left( x ^ { 2 } - 3 x - 2 \right) + 4\).

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Definitions:

Average Total Cost

The average cost per unit of output, calculated by dividing the total production cost by the quantity of goods produced.

Fixed Cost

Expenses that do not change with the level of production or sales over a certain period, such as rent or salaries.

Output

The amount of goods or services produced by a person, machine, or industry.

Marginal Product

Marginal product refers to the additional output generated by employing one more unit of a specific factor of production, holding all other factors constant.