Resolve each of the following quadratic trinomial into factor:
Question:

Resolve each of the following quadratic trinomial into factor:
7x − 6 − 2x2

Solution:

The given expression is $7 \mathrm{x}-6-2 \mathrm{x}^{2}$. (Coefficient of $\mathrm{x}^{2}=-2$, coefficient of $\mathrm{x}=7$ and constant term$=-6$ )

We will split the coefficient of $\mathrm{x}$ into two parts such that their sum is 7 and their product equals the product of the coefficient of $\mathrm{x}^{2}$ and the constant term, i.e., $(-2) \times(-6)=12$.

Now,

$4+3=7$

and

$4 \times 3=12$

Replacing the middle term $7 \mathrm{x}$ by $4 \mathrm{x}+3 \mathrm{x}$, we have :

$7 \mathrm{x}-6-2 \mathrm{x}^{2}=-2 \mathrm{x}^{2}+4 \mathrm{x}+3 \mathrm{x}-6$

$=\left(-2 \mathrm{x}^{2}+4 \mathrm{x}\right)+(3 \mathrm{x}-6)$

$=2 \mathrm{x}(2-\mathrm{x})-3(2-\mathrm{x})$

$=(2 \mathrm{x}-3)(2-\mathrm{x})$