Factor Completely $$p ^ { 6 } + q ^ { 24 } r ^ { 18 }$$

question 72

Multiple Choice

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
- $$p ^ { 6 } + q ^ { 24 } r ^ { 18 }$$

• A) \(\left( p + q ^ { 4 } r ^ { 3 } \right) \left( p - q ^ { 4 } r ^ { 3 } \right) \left( p ^ { 4 } - p ^ { 2 } q ^ { 8 } r ^ { 6 } + q ^ { 16 } r ^ { 12 } \right)\)
• B) \(\left( \mathrm { p } ^ { 3 } + \mathrm { q } ^ { 12 } \mathrm { r } ^ { 9 } \right) \left( \mathrm { p } ^ { 3 } - \mathrm { q } ^ { 12 } \mathrm { r } ^ { 9 } \right)\)
• C) \(\left( p + q ^ { 4 } r ^ { 3 } \right) \left( p - q ^ { 4 } r ^ { 3 } \right) \left( p ^ { 2 } + p q ^ { 4 } r ^ { 3 } + q ^ { 8 } r ^ { 6 } \right) \left( p ^ { 2 } - q ^ { 4 } r ^ { 3 } + q ^ { 8 } r ^ { 6 } \right)\)
• D) \(\left( p ^ { 2 } + q ^ { 8 } r ^ { 6 } \right) \left( p ^ { 4 } - p ^ { 2 } q ^ { 8 } r ^ { 6 } + q ^ { 16 } r ^ { 12 } \right)\)

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Definitions:

Core Nations

Countries that dominate global trade and economics, often through technological advancement and wealth.

Peripheral Countries

Nations that are less developed than the semi-peripheral and core countries, often characterized by low levels of industrialization, and significant economic dependence on core countries.

World Systems Theory

A framework for understanding the historical and contemporary social structures of global inequality, delineating countries as core, periphery, or semi-periphery.

Modernization Theory

A theory in sociology that suggests that societies progress from traditional to modern states through processes like industrialization and democratization, improving living standards and social norms.