3 + 23y – 8y2 = - 8y2 + 23y + 3
Here, coefficient of y2 = -8, coefficient of y = 23 and constant term = 3
We shall now split up the coefficient of x i.e., 23 into two parts whose sum is 23 and product is -8 (3) = - 24
Clearly,
24 - 1 = 23 and
24 (-1) = - 24
So, we write middle term 23y as 24y - y
Thus, we have
- 8y2 + 23y + 3 = - 82 + 24y - y + 3
= - 8y (y – 3) - 1 (y – 3)
= - (8y + 1) (y – 3)