Completely Factor the Polynomial or State That the Polynomial Is $$343 x ^ { 3 } + 512$$

question 189

Multiple Choice

Completely factor the polynomial or state that the polynomial is prime.
- $$343 x ^ { 3 } + 512$$

• A) \(( 7 x - 8 ) \left( 49 x ^ { 2 } + 56 x + 64 \right)\)
• B) \(( 7 x + 8 ) \left( 49 x ^ { 2 } - 56 x + 64 \right)\)
• C) \(( 343 x - 8 ) \left( x ^ { 2 } + 56 x + 64 \right)\)
• D) \(( 7 x + 8 ) \left( 49 x ^ { 2 } + 56 x + 64 \right)\)

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Definitions:

Cyclopentane

A cycloalkane with the molecular formula C5H10, consisting of a ring of five carbon atoms each connected with two hydrogen atoms, used as a solvent and in organic synthesis.

Cyclopentene

A cyclic hydrocarbon with the molecular formula C5H8, featuring a five-membered ring with one double bond.

Ammonia

A compound of nitrogen and hydrogen with the formula NH3, known for its pungent smell and use as a nitrogen source in fertilizers.

Triethylamine

A strong, organic base with the formula (C2H5)3N, used as a catalyst and solvent in chemical synthesis.