Resolve each of the following quadratic trinomial into factor:
2x2 − 3x − 2
The given expression is $2 x^{2}-3 x-2$. (Coefficient of $\mathrm{x}^{2}=2$, coefficient of $\mathrm{x}=-3$ and constant term $=-2$ )
We will split the coefficient of $\mathrm{x}$ into two parts such that their sum is $-3$ and their product equals the product of the coefficient of $\mathrm{x}^{2}$ and the constant term, i.e., $2 \times(-2)=-4$.
Now,
$(-4)+1=-3$
and
$(-4) \times 1=-4$
Replacing the middle term $3 \mathrm{x}$ by $-4 \mathrm{x}+\mathrm{x}$, we have:
$2 x^{2}-3 x-2=2 x^{2}-4 x+x-2$
$=\left(2 \mathrm{x}^{2}-4 \mathrm{x}\right)+(\mathrm{x}-2)$
$=2 \mathrm{x}(\mathrm{x}-2)+(\mathrm{x}-2)$
$=(2 \mathrm{x}+1)(\mathrm{x}-2)$
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