Partial grouping with Venn diagrams

Example — Factorise $x^2 - 3x - 2x + 6$ with the circle method

I group in pairs and represent the factors of each term with overlapping circles: in the common region sits the factor shared by the pair.

In each pair the overlap region is the common factor; the “remainders” outside the overlap form the second factor.

The “remainders” of each pair form the second factor, so: $x^2 - 3x - 2x + 6 = x(x-3) - 2(x-3) = \boxed{(x-3)(x-2)}$

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Topics: Algebraic calculation
Concepts: Partial grouping · Factorisation
Skills: Factorising