Factorise the following:

x² + 5x + 6

To factorise x² + 5x + 6, we want to find two real numbers whose sum is 5 and product is 6. By trial, we see that 2 + 3 = 5 and 2 × 3 = 6.

∴ x² + 5x + 6 = x² + 2x + 3x + 6

= x(x + 2) + 3(x + 2)

= (x + 3)(x + 2).

Hence, x² + 5x + 6 = (x + 3)(x + 2).