Factor the Greatest Common Factor from the Polynomial $$42 x ^ { 8 } y ^ { 6 } z ^ { 2 } - 36 x ^ { 3 } y ^ { 4 } z ^ { 3 } - 36 x ^ { 5 } y ^ { 2 } z ^ { 4 }$$

question 61

Multiple Choice

Factor the greatest common factor from the polynomial. Assume any variable exponents represent whole numbers.
- $$42 x ^ { 8 } y ^ { 6 } z ^ { 2 } - 36 x ^ { 3 } y ^ { 4 } z ^ { 3 } - 36 x ^ { 5 } y ^ { 2 } z ^ { 4 }$$

• A) \(6 x ^ { 3 } y ^ { 2 } z ^ { 3 } \left( 7 x ^ { 5 } y ^ { 4 } - 6 y ^ { 2 } - 6 x ^ { 2 } z \right)\)
• B) \(6 x ^ { 3 } y ^ { 2 } z ^ { 2 } \left( 7 x ^ { 5 } y ^ { 4 } - 6 y ^ { 2 } z - 6 x ^ { 2 } z ^ { 2 } \right)\)
• C) \(x ^ { 3 } y ^ { 2 } z ^ { 2 } \left( 42 x ^ { 5 } y ^ { 4 } - 36 y ^ { 2 } z - 36 x ^ { 2 } z ^ { 2 } \right)\)
• D) \(6 \left( 7 x ^ { 8 } y ^ { 6 } z ^ { 2 } - 6 x ^ { 3 } y ^ { 4 } z ^ { 3 } - 6 x ^ { 5 } y ^ { 2 } z ^ { 4 } \right)\)

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Definitions:

Stability

The resistance of a chemical substance to decomposition or chemical change.

Primary Alkyl Halides

Organic compounds where a halogen atom is directly bonded to a primary carbon, which is attached to only one other carbon.

Secondary Alkyl Halide

An organic compound in which a halogen atom is bonded to a secondary carbon, i.e., a carbon atom connected to two other carbon atoms.

Dichlorination Products

The chemical compounds resulting from the addition of two chlorine atoms to another molecule, often used in the context of organic chemistry reactions.