Solve the Inequality $$9 x ^ { 3 } + 36 x ^ { 2 } - 16 x - 64 > 0$$

question 188

Multiple Choice

Solve the inequality. Write the solution set in interval notation.
- $$9 x ^ { 3 } + 36 x ^ { 2 } - 16 x - 64 > 0$$

• A) \(\left( - 4 , - \frac { 4 } { 3 } \right) \cup \left( \frac { 4 } { 3 } , \infty \right)\)
• B) \(\left[ - 4 , - \frac { 4 } { 3 } \right] \cup \left[ \frac { 4 } { 3 } , \infty \right)\)
• C) \(( - \infty , - 4 ] \cup \left[ - \frac { 4 } { 3 } , \frac { 4 } { 3 } \right]\)
• D) \(( - \infty , - 4 ) \cup \left( - \frac { 4 } { 3 } , \frac { 4 } { 3 } \right)\)

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Definitions:

Dielectric

An insulating material that can be polarized by an electric field, enhancing the capacitor's ability to store an electric charge.

Mica

A mineral used as an electric insulator.

Northwest Ordinance

An act passed by the Confederation Congress in 1787 that established a government for the Northwest Territory and outlined the process for admitting new states to the Union, prohibiting slavery in the territory.

Old Northwest

A historical term referring to the territory that became the states of Ohio, Indiana, Illinois, Michigan, Wisconsin, and parts of Minnesota; it was an important region for expansion and settlement in early U.S. history.