Factorise : $6 x^{2} + 17 x + 12$

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Solution

Factorise : $6 x^{2} + 17 x + 12$ using common method.
$6 x^{2} + 17 x + 12$
The coefficient of $x^{2}$ is $6$ and constant is $12.$ The product of two coefficients $= 6 \times 12 = 72$
Now, the coefficient of middle term $= 17$
We know, that the factors of $72$ such that the sum of these factors is $17$ are $8 & 9 (8 \times 9 = 72, 8 + 9 = 17)$
So, $6 x^{2} + 8 x + 9 x + 12$
$\Rightarrow 2 x (3 x + 4) + 3 (3 x + 4)$
$\Rightarrow (2 x + 3) (3 x + 4) .$
Hence, the answer is $(2 x + 3) (3 x + 4) .$

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