Factor a polynomial by grouping to reveal a common binomial or polynomial factor
Problem
Factor \(x^3~+~2x^2~+~3x~+~6\) completely by grouping.
Big Picture
What this problem is really about
Factoring by grouping is a two-level common-factor search. First pair terms so each group can release its own greatest common factor; if both groups then expose the same binomial, treat that whole binomial as one shared unit and factor it out. Expanding the resulting product verifies both the grouping and the signs.
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