Factorisation of quadratic expressions

For a quadratic expression of the form $ax^2 + bx + c$, we look for two numbers that multiply to $a \times c$ and add up to $b$.

Let's take an example: Factorise $x^2 + 5x + 6$.
Here, $a=1$, $b=5$, and $c=6$.
We need two numbers that multiply to $a \times c = 1 \times 6 = 6$ and add up to $b=5$.
The numbers are 2 and 3, because $2 \times 3 = 6$ and $2 + 3 = 5$.