Factoring by grouping is a method for factoring a polynomial, most often one with four terms, by splitting it into pairs. Learn the steps: group the terms into pairs, factor the greatest common factor from each pair, then factor out the shared binomial, with a worked example.
What factoring by grouping is
Factoring by grouping is a method for factoring a polynomial — most often one with four terms — by splitting it into pairs and pulling a common factor out of each pair. It builds on factoring out the greatest common factor, applied one group at a time.
The steps
Factoring by grouping: group into pairs, factor each pair, then factor out the common binomial.
Group the terms into two pairs, factor the greatest common factor from each pair, and if the pairs now share the same binomial, factor that binomial out. Recognizing shared factors relies on spotting the common factors of polynomials.
Worked example
Factor x³ + 3x² + 2x + 6. Group as (x³ + 3x²) + (2x + 6). Factor each pair: x²(x + 3) + 2(x + 3). Both share (x + 3), so the result is (x + 3)(x² + 2).
When it works
Grouping works when the pairs produce a shared binomial. If they do not, try reordering the terms first. Grouping is one tool among several, alongside patterns like the difference of squares.