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

1.	Resolve each of the following quadratic trinomials into factors: 7x - 6 - 2x2
Answer» 7x - 6 - 2x² = - 2x² + 7x – 6 Here, coefficient of x² = - 2, coefficient of x = 7 and constant term = -6 We shall now split up the coefficient of x i.e., 7 into two parts whose sum is 7 and product is - 2 x - 6 = 12 Clearly, 4 + 3 = 7 and 4 x 3 = 12 So, we write middle term 7x as 4x + 3x Thus, we have - 2x² + 7x – 6 = - 2x² + 4x + 3x – 6 = - 2x (x – 2) + 3 (x – 2) = (x – 2) (3 – 2x) f(x)=-2x²+7x-6 =>-f(x)=2x²-7x+6 =>-f(x)=2x²-3x-4x+6 =>-f(x)=x(2x-3)-2(2x-3) =>-f(x)=(2x-3)(x-2) =>f(x)=(2x-3)(2-x)

Resolve each of the following quadratic trinomials into factors: 7x - 6 - 2x2

Answer»

7x - 6 - 2x² = - 2x² + 7x – 6

Here, coefficient of x² = - 2, coefficient of x = 7 and constant term = -6

We shall now split up the coefficient of x i.e., 7 into two parts whose sum is 7 and product is - 2 x - 6 = 12

Clearly,

4 + 3 = 7 and

4 x 3 = 12

So, we write middle term 7x as 4x + 3x

Thus, we have

- 2x² + 7x – 6 = - 2x² + 4x + 3x – 6

= - 2x (x – 2) + 3 (x – 2)

= (x – 2) (3 – 2x)

f(x)=-2x²+7x-6

=>-f(x)=2x²-7x+6

=>-f(x)=2x²-3x-4x+6

=>-f(x)=x(2x-3)-2(2x-3)

=>-f(x)=(2x-3)(x-2)

=>f(x)=(2x-3)(2-x)