Question

Resolve each of the following quadratic trinomials into factors:

28 - 31x - 5x²

Answer 1

28 – 31x – 5x² = - 5x² – 31x + 28

Here, coefficient of x² = -5, coefficient of x = - 31 and constant term = 28

We shall now split up the coefficient of x i.e., - 31 into two parts whose sum is - 31 and product is -5 (28) = - 140

Clearly,

4 - 35 = - 31 and

4 (-35) = - 140

So, we write middle term - 31x as 4x - 35x

Thus, we have

– 5x² – 31x + 28 = -5x² + 4x - 35x + 28

= -x (5x – 4) - 7 (5x – 4)

= - (x + 7) (5x - 4)