Factoring by grouping involves reorganizing a polynomial, typically with four terms, into pairs whose terms share a greatest common monomial factor; after factoring each pair, the resulting expressions reveal a common binomial factor that can be extracted using the distributive property. This connects expansion and factoring as inverse processes and requires careful attention to signs and equivalent rearrangements. The scope is standard low-degree polynomial expressions, not advanced multivariable or abstract factorization methods.
Factoring by grouping works best when a polynomial has four terms. Group the terms into two pairs, factor out the greatest common factor from each pair, and then look for a common binomial factor.
Example: Factor
Step 1: Group the terms in pairs.
Step 2: Factor out the greatest common factor from each pair.
From , the greatest common factor is :
From , the greatest common factor is :
So the expression becomes
Step 3: Factor out the common binomial.
Both terms contain :
You can check by multiplying:
Therefore,
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