Factorise the following:

2y² + y - 45

To factorise 2y² + y - 45, we want to find two real numbers whose sum is 1 and product is 2 × (-45) = -90. By trial, we see that 10 - 9 = 1 and 10 × (-9) = -90.

∴ 2y² + y - 45 = 2y² + 10y + (-9y) - 45

= 2y² + 10y - 9y - 45

= 2y(y + 5) - 9(y + 5)

= (y + 5)(2y - 9).

Hence, 2y² + y - 45 = (y + 5)(2y - 9).