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Factorise by grouping

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Factoring by Grouping

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.

Factoring by grouping, step by step Worked example. Start with x cubed plus 3 x squared plus 2 x plus 6. Group into (x cubed plus 3 x squared) plus (2 x plus 6). Factor each pair: x squared times (x plus 3) plus 2 times (x plus 3). Factor out the common binomial (x plus 3) to get (x plus 3)(x squared plus 2). 1. Group into pairs (x³ + 3x²) + (2x + 6) 2. Factor each pair x²(x + 3) + 2(x + 3) 3. Factor out the common binomial (x + 3) (x + 3)(x² + 2)
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.

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).

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.

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