Factorise by splitting middle term
$12 x^{2} - 7 x + 1$

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Solution

Let $p (x) = 12 x^{2} - 7 x + 1$
Here we have to split middle term $- 7$ into two parts such that their sum is $- 7$ and product is $12 \times 1 = 12$
$- 4$ and $- 3$ are such numbers whose sum is $- 7$ and product is $12$
$12 x^{2} - 7 x + 1 = 12 x^{2} - 4 x - 3 x + 1$
$= 4 x (3 x - 1) - 1 (3 x - 1)$
$= (3 x - 1) (4 x - 1)$

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