Factorise :
$2 x^{2} + 7 x + 3$

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Solution

Given quadratic expression is $2 x^{2} + 7 x + 3$
Since, $2 x^{2} \times 3 = 6 x^{2}$ and Middle term $= 7 x$
Here, we need to select two terms, such that their sum is $7 x$ and their product is $6 x^{2}$ .
Clearly $6 x + x = 7 x$ and $6 x \times x = 6 x^{2}$
Hence, the two terms are $6 x$ and $x$ .
Now, lets factorize by splitting the middle term,
$2 x^{2} + 7 x + 3$
$= 2 x^{2} + 6 x + x + 3$
$= 2 x (x + 3) + (x + 3)$
$= (2 x + 1) (x + 3)$
$∴ 2 x^{2} + 7 x + 3 = (2 x + 1) (x + 3)$ .

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