Factorise the following:

2x² - 7x + 6

To factorise 2x² - 7x + 6, we want to find two real numbers whose sum is -7 and product is 2 × 6 = 12. By trial, we see that (-4) + (-3) = -7 and -4 × -3 = 12.

∴ 2x² - 7x + 6 = 2x² - 4x + (-3x) + 6

= 2x² - 4x - 3x + 6

= 2x(x - 2) - 3(x - 2)

= (x - 2)(2x - 3).

Hence, 2x² - 7x + 6 = (x - 2)(2x - 3).