Use expression structure to identify useful rewrites, such as difference-of-squares factoring.
Factor by grouping
Problem
Factor \(x^{3}+3x^{2}+2x+6\) by grouping. Pair the terms, extract each group’s GCF so the same binomial appears, factor that binomial, and expand the final product to verify it.
Big Picture
What this problem is really about
Factoring by grouping succeeds when the term pairs can expose the same binomial. We’ll group the polynomial in pairs, extract each group’s greatest common factor, factor the shared binomial from the two resulting terms, and expand the product to verify every original term and sign.
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