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Factors of Natural Numbers

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Question

Factorise the trinomial $2 x^{2} + 7 x + 6$ .

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Solution

Given trinomial = $2 x^{2} + 7 x + 6$
The product of the first and the last term = $2 x^{2} \times 6$ = $12 x^{2}$ .
Splitting the middle term 7x into two terms such a way that their product is $12 x^{2}$ and sum is 7x. The terms are 3x and 4x.
$2 x^{2} + 7 x + 6$ = $2 x^{2} + 4 x + 3 x + 6$
= $2 x (x + 2) + 3 (x + 2)$ = $(x + 2) (2 x + 3)$

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