Factorize : $2 x^{4} + x^{3} - 14 x^{2} - 19 x - 6$

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Solution

Consider given the expression,

$\Rightarrow 2 x^{4} + x^{3} - 14 x^{2} - 19 x - 6$

$\Rightarrow x^{3} (2 x + 1) - (14 x^{2} + 19 x + 6)$

$\Rightarrow x^{3} (2 x + 1) - (14 x^{2} + 7 x + 12 x + 6)$

$\Rightarrow x^{3} (2 x + 1) - [7 x (2 x + 1) + 6 (2 x + 1)]$

$\Rightarrow x^{3} (2 x + 1) - (2 x + 1) (7 x + 6)$

$\Rightarrow (2 x + 1) (x^{3} - 7 x - 6)$

Hence, this is the answer.

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