If $x = \sqrt { 7 } \text { is a root of } x ^ { 3 } - 3 x ^ { 2 } - 7 x + 21 = 0$

question 93

Multiple Choice

If $x = \sqrt { 7 } \text { is a root of } x ^ { 3 } - 3 x ^ { 2 } - 7 x + 21 = 0$ , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

• A) \(( x - 3 ) ( x - \sqrt { 7 } ) ( x + \sqrt { 7 } ) ; 3 , \sqrt { 7 } , - \sqrt { 7 }\)
• B) \(( x + 3 ) ( x + \sqrt { 7 } ) ^ { 2 } ; - 3 , \sqrt { 7 }\)
• C) \(( x + 3 ) ( x - \sqrt { 7 } ) ^ { 2 } ; - 3 , \sqrt { 7 }\)
• D)\(( x + 3 ) ( x + \sqrt { 7 } ) ^ { 2 } ; 3 , - \sqrt { 7 }\)
• E) \(( x + 3 ) ^ { 2 } ( x - \sqrt { 7 } ) ; - 3 , \sqrt { 7 }\)

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Definitions:

Phenomenological

This term relates to a philosophical and research approach that focuses on exploring and describing experiences exactly as they are perceived, without interpretation or assumption.

Postmodern

A broad movement in philosophy, art, architecture, and criticism that emerged in the mid-to-late 20th century, characterized by skepticism towards grand narratives and ideologies.

Philosophical Schools

Different traditions or approaches within philosophy that are characterized by distinct theories and methodologies.

Systemic

Pertains to viewing problems or solutions as part of a comprehensive system, recognizing the interdependencies and interactions between parts of the system.