Factorising a trinomial with sum and product

Example — Factorise $x^2-5x+6$

I look for two numbers with sum $-5$ and product $6$: they are $-3$ and $-2$.

Check: $(-3)+(-2) = -5$ ✓, $\;(-3)\cdot(-2)=6$ ✓.

Method: we split the middle term and use partial grouping.

We split $-5x$ into $-3x-2x$, group in pairs and find the common factor $(x-3)$.

Therefore $x^2 - 5x + 6 = \boxed{(x-3)(x-2)}$.

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