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The LCM of the polynomials $12 (x^{4} - x^{3})$ and $(x^{4} - 3 x^{3} + 2 x^{2})$ is $k x^{3} (x - 1) (x - 2)$ , then $k$ is

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Detailed Solution

$\begin{array}{l} p (x) = 12 (x^{4} - x^{3}) \\ q (x) = x^{4} - 3 x^{3} + 2 x^{2} \\ p (x) = 12 x^{3} (x - 1) \\ q (x) = x^{2} (x^{2} - 3 x + 2) \\ = x^{2} (x - 1) (x - 2) \end{array}$

$∴$ LCM of $p (x) & q (x)$ is $12 x^{3} (x - 1) (x - 2)$

$K x^{3} (x - 1) (x - 2) = 12 x^{3} (x - 1) (x - 2)$

$K = 12$

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