Given the Polynomial Function F(x), Find the Rational Zeros, Then $$f ( x ) = \frac { 1 } { 2 } x ^ { 3 } - \frac { 2 } { 3 } x ^ { 2 } - \frac { 1 } { 12 } x + \frac { 1 } { 12 }$$

question 47

Multiple Choice

Given the polynomial function f(x) , find the rational zeros, then the other zeros (that is, solve the equation f(x) = 0) , and
factor f(x) into linear factors.
- $$f ( x ) = \frac { 1 } { 2 } x ^ { 3 } - \frac { 2 } { 3 } x ^ { 2 } - \frac { 1 } { 12 } x + \frac { 1 } { 12 }$$

• A) \(\frac { 1 } { 3 } , \frac { 1 + \sqrt { 3 } } { 2 } , \frac { 1 - \sqrt { 3 } } { 2 } ; f ( x ) = \left( x - \frac { 1 } { 3 } \right) \left( x - \frac { 1 + \sqrt { 3 } } { 2 } \right) \left( x - \frac { 1 - \sqrt { 3 } } { 2 } \right)\)
• B) \(\frac { 1 } { 2 } , \frac { 1 + \sqrt { 3 } } { 2 } , \frac { 1 - \sqrt { 3 } } { 2 } ; f ( x ) = \left( \frac { 1 } { 3 } \right) \left( x - \frac { 1 } { 3 } \right) \left( x - \frac { 1 + \sqrt { 3 } } { 2 } \right) \left( x - \frac { 1 - \sqrt { 3 } } { 2 } \right)\)
• C) \(\frac { 1 } { 2 } , \frac { 1 + \sqrt { 2 } } { 2 } , \frac { 1 - \sqrt { 2 } } { 2 } ; f ( x ) = \left( x - \frac { 1 } { 2 } \right) \left( x - \frac { 1 + \sqrt { 2 } } { 2 } \right) \left( x - \frac { 1 - \sqrt { 2 } } { 2 } \right)\)
• D) \(\frac { 1 } { 3 } , \frac { 1 + \sqrt { 3 } } { 2 } , \frac { 1 - \sqrt { 3 } } { 2 } ; f ( x ) = \left( \frac { 1 } { 2 } \right) \left( x - \frac { 1 } { 3 } \right) \left( x - \frac { 1 + \sqrt { 3 } } { 2 } \right) \left( x - \frac { 1 - \sqrt { 3 } } { 2 } \right)\)

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Definitions:

Institutional Racism

The systemic distribution of resources, power, and opportunity in our society to the benefit of people who are white and the exclusion of people of color.

De Jure Segregation

Legal separation of groups of people based on law, such as racial segregation that's enforced by legislation.

De Facto Segregation

Racial segregation that occurs not by law, but as a result of voluntary associations and neighborhoods, along with other factors like economic or social conditions.

Disavow Prejudice

The act of denying or renouncing any prejudiced beliefs or attitudes one might hold.