Use Synthetic Division $$f ( x ) \text { by } x - k \text { for the given value of } k \text {. Then express } f ( x ) \text { in the form } f ( x ) = ( x - k ) q ( x ) + r$$

question 109

Multiple Choice

Use synthetic division $$f ( x ) \text { by } x - k \text { for the given value of } k \text {. Then express } f ( x ) \text { in the form } f ( x ) = ( x - k ) q ( x ) + r$$ for the given value of k.
- $$f ( x ) = - 6 x ^ { 3 } + 2 x ^ { 2 } + 5 x - 10 ; \quad k = 2$$

• A) \(f ( x ) = ( x + 2 ) \left( - 6 x ^ { 2 } + 10 x + 25 \right) - 40\)
• B) \(f ( x ) = ( x - 2 ) \left( - 6 x ^ { 2 } - 10 x + 15 \right) - 40\)
• C) \(f ( x ) = ( x - 2 ) \left( - 6 x ^ { 2 } + 10 x + 25 \right) - 40\)
• D) \(f ( x ) = ( x - 2 ) \left( - 6 x ^ { 2 } - 10 x - 15 \right) - 40\)

---

Definitions:

Associated

Pertains to the connection or relationship between two or more variables or factors.

Response Variable

The outcome or variable of interest that is measured or observed in a study, experiment, or analysis to see how it is affected by explanatory variables.

Fuel Efficiency

The measure of how far a vehicle can travel per unit of fuel.

Miles Per Gallon

A measure of a vehicle's fuel efficiency, indicating how many miles it can travel on one gallon of fuel.