Question

Resolve each of the following quadratic trinomials into factors:

7x² - 19x - 6

Answer 1

Here, coefficient of x² = 7, coefficient of x = -19 and constant term = -6

We shall now split up the coefficient of x i.e., -19 into two parts whose sum is -19 and product is 7 x -6 = -42

Clearly, 2 - 21 = -19 and

2 x (-21) = - 42

So, we write middle term - 19x as 2x - 21x

Thus, we have

7x² - 19x – 6 = 7x² + 2x - 21x – 6

= x (7x + 2) - 3 (7x + 2)

= (7x + 2) (x – 3)