Resolve each of the following quadratic trinomials into factors:
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 * -6 = -42
Clearly,
2 - 21 = -19 and,
2 * (-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)