Resolve each of the following quadratic trinomials into factors:3 + 23

1.	Resolve each of the following quadratic trinomials into factors:3 + 23y - 8y2
Answer» 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)

Resolve each of the following quadratic trinomials into factors:3 + 23y - 8y2

Answer»

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)