Write $f ( x ) = x ^ { 3 } - 11 x ^ { 2 } + 18 x + 25$

question 43

Multiple Choice

Write $f ( x ) = x ^ { 3 } - 11 x ^ { 2 } + 18 x + 25$ in the form $f ( x ) = ( x - k ) q ( x ) + r$ when $k = 6 + \sqrt { 6 }$ .

• A) \(f ( x ) = [ x + ( 6 + \sqrt { 6 } ) ] \left[ x ^ { 2 } + ( - 5 + \sqrt { 6 } ) x - ( 6 - \sqrt { 6 } ) \right] - 5\)
• B) \(f ( x ) = [ x + ( 6 + \sqrt { 6 } ) ] \left[ x ^ { 2 } + ( - 5 + \sqrt { 6 } ) x - ( 6 - \sqrt { 6 } ) \right] + 5\)
• C) \(f ( x ) = [ x - ( 6 + \sqrt { 6 } ) ] \left[ x ^ { 2 } + ( - 5 + \sqrt { 6 } ) x - ( 6 - \sqrt { 6 } ) \right] + 5\)
• D) \(f ( x ) = [ x - ( 6 + \sqrt { 6 } ) ] \left[ x ^ { 2 } + ( - 5 + \sqrt { 6 } ) x - ( 6 - \sqrt { 6 } ) \right] - 5\)
• E) \(f ( x ) = [ x + ( 6 + \sqrt { 6 } ) ] \left[ x ^ { 2 } - ( - 5 + \sqrt { 6 } ) x - ( 6 - \sqrt { 6 } ) \right] - 5\)

---

Definitions:

Economic Functions

The roles and operations performed by an economic system, such as allocation of resources, distribution of income, and stabilization of the economy.

U.S. Government

The federal government of the United States, composed of three distinct branches: legislative, executive, and judicial, as established by the Constitution.

Issues Regulations

Rules and guidelines issued by authorities to control or govern behaviors and operations in various sectors.

Mixed Economy

An economic system that combines elements of capitalism and socialism, including both private and public ownership of resources and enterprises.