Madhya Pradesh Police Exam Model Paper 10

Tips & Tricks
Given :-
The factors of the expression $2{\mathit{x}}^2-5\mathit{x}-12$
Concept :-
To factorize a given trinomial following steps should be adopted :
(1) Find the product of the first and the last terms of the trinomial with their signs.
(2) Split the middle term of the given trinomial such that the sum of these two terms is equal to the middle term and their product is equal to the product of first and last terms.
(3) Forming the suitable groups.
Calculation :-
$\Rightarrow 2{\mathit{x}}^2-5\mathit{x}-12$ ⇒ First term $=2{\mathit{x}}^2$
⇒ Second term $=-5\mathit{x}$
⇒ Third term = - 12
⇒ Product of first and last term $=2{\mathit{x}}^2\times -12$ ⇒ Product of first and last term $=-24{\mathit{x}}^2$ Now split the second term into two term such that sum is equal to -5x and product of their term $-24{\mathit{x}}^2$ $\Rightarrow -5\mathit{x}=-8\mathit{x}+3\mathit{x}$
Now,
$\Rightarrow 2\mathit{x}\left(\mathit{x}-4\right)+3\left(\mathit{x}-4\right)$
$\Rightarrow \left(\mathit{x}-4\right)\times \left(2\mathit{x}+3\right)$
⇒ Factors are $\left(\mathit{x}-4\right)\mathrm{and}\left(2\mathit{x}+3\right)$
∴ Factors are $\left(\mathit{x}-4\right)\mathrm{and}\left(2\mathit{x}+3\right)$