Resolve each of the following quadratic trinomials into factors:7x2 -

1.	Resolve each of the following quadratic trinomials into factors:7x2 - 19x - 6
Answer» 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)

Resolve each of the following quadratic trinomials into factors:7x2 - 19x - 6

Answer»

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)