Factorise the following:

6x² + 13x - 5

To factorise 6x² + 13x - 5, we want to find two real numbers whose sum is 13 and product is 6 × (-5) = -30. By trial, we see that 15 + (-2) = 13 and 15 × -2 = -30.

∴ 6x² + 13x - 5 = 6x² + 15x + (-2x) - 5

= 6x² + 15x - 2x - 5

= 3x(2x + 5) - 1(2x + 5)

= (2x + 5)(3x - 1).

Hence, 6x² + 13x - 5 = (2x + 5)(3x - 1).