Problem

Factor \(2x^{3}-6x^{2}+5x-15\) by grouping. Extract the correct GCF from each pair so both contain \(x-3\), factor the shared binomial, and confirm the product by expansion.

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grouping=(2x³−6x²)+(5x−15); group GCFs=2x²(x−3)+5(x+3); common binomial=none because signs differ; final factorization=not possible by this grouping; expansion check=does not recover original

grouping=(2x³−6x²)+(5x−15); group GCFs=2x²(x−3)+5(x−3); common binomial=x−3; final factorization=2x²(x−3)+5(x−3); expansion check=original

grouping=(2x³−6x²)+(5x−15); group GCFs=2x²(x−3)+5(x−3); common binomial=x−3; factored=(x−3)(2x²+5); expansion check=original

grouping=(2x³−6x²)+(5x−15); group GCFs=2x²(x−3)+5(x−3); common binomial=x−3; final factorization=(x−3)+(remaining terms); expansion check=does not recover original

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Factor \(2x^{3}-6x^{2}+5x-15\) by grouping. Extract the correct GCF from each pair so both contain \(x-3\), factor the shared binomial, and confirm the product by expansion.

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