Write the Polynomial as the Product of Linear and Quadratic $\left( x ^ { 2 } + 49 \right) ( x + \sqrt { 7 } ) ( x - 7 )$

question 16

Multiple Choice

Write the polynomial as the product of linear and quadratic factors that are irreducible over the reals.
F(x) = x⁴ + 42x² - 343

• A) \(\left( x ^ { 2 } + 49 \right) ( x + \sqrt { 7 } ) ( x - 7 )\)
• B) \(\left( x ^ { 2 } + 49 \right) ( x + \sqrt { 7 } ) ( x + \sqrt { 7 } )\)
• C) \(\left( x ^ { 2 } + 49 \right) ( x - \sqrt { 7 } ) ( x - \sqrt { 7 } )\)
• D) \(\left( x ^ { 2 } + 49 \right) ( x + \sqrt { 7 } ) ( x - \sqrt { 7 } )\)
• E) \(\left( x ^ { 2 } + 49 \right) ( x + 7 ) ( x - \sqrt { 7 } )\)

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Definitions:

Consequent

In logic, the latter part of a conditional statement, the outcome or result that follows the condition specified in its antecedent.

Antecedent

In logic and grammar, the preceding statement or element that provides the context for a subsequent statement or element.

Proposition

A statement or assertion that expresses a judgment or opinion, or in logic, the content of an assertion that can be true or false.

Standard Form

A recognized format for presenting arguments or statements in a structured and consistent manner.