Factorise the following:

5 - 4x - 12x²

To factorise 5 - 4x - 12x², we want to find two real numbers whose sum is -4 and product is 5 × (-12) = -60. By trial, we see that -10 + 6 = -4 and (-10) × 6 = -60.

∴ 5 - 4x - 12x² = 5 - 10x + 6x - 12x²

= 5(1 - 2x) + 6x(1 - 2x)

= (1 - 2x)(5 + 6x).

Hence, 5 - 4x - 12x² = (1 - 2x)(5 + 6x).