The special trinomial - sum and product method

A particularly elegant technique for factorising second-degree trinomials is the sum and product method: we look for two numbers whose sum and product match the coefficients of the trinomial.

Property — Special trinomial

To factorise $x^2+sx+p$, we look for two numbers $a$ and $b$ such that: $a+b = s \quad\text{(somma)}, \qquad a\cdot b = p \quad\text{(prodotto)}.$ Then: $x^2+sx+p = (x+a)(x+b).$

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