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Factor.
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Q. Factor.
- Identify GCF: Step Title: Identify the Greatest Common Factor (GCF) Concise Step Description: Determine the greatest common factor of all the terms in the polynomial. Step Calculation: The GCF of , , , and is . Step Output: GCF:
- Group Terms: Step Title: Group TermsConcise Step Description: Group terms in pairs to facilitate factoring by grouping.Step Calculation: Group the terms as and .Step Output: Grouped Terms: and
- Factor by Grouping: Step Title: Factor by GroupingConcise Step Description: Factor out the common factors from each group.Step Calculation: Factor out from the first group and from the second group.Step Output: Factored Groups:
- Factor Common Binomial: Step Title: Factor Out the Common BinomialConcise Step Description: Factor out the common binomial factor from the two groups.Step Calculation: The common binomial factor is .Step Output: Factored Polynomial:
- Factor Further: Step Title: Factor Further if PossibleConcise Step Description: Check if the remaining quadratic can be factored further.Step Calculation: The quadratic is a difference of squares and can be factored as .Step Output: Fully Factored Polynomial: $(\(3\)x - \(1\))(\sqrt{\(6\)}x - \(1\))(\sqrt{\(6\)}x + \(1\))
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