Find the polynomial which is equivalent to:
$12 x^{2} y^{3} z^{4} - 30 x y^{2} + 24 x^{2} y^{5} z$ ?

6 x y^{2} (2 y z^{3} - 5 + 4 x y^{3})

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6 x y^{2} (2 x y z^{4} - 5 + 4 x y^{3} z)

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6 x y^{2} z (2 x y z^{3} - 5 + 4 x y^{3})

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12 x^{2} y^{3} (y z^{4} - 5 + 2 y^{2} z)

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12 x^{2} y^{3} z (x y^{2} z^{3} - 5 z + 2 y^{2})

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Solution

The correct option is B $6 x y^{2} (2 x y z^{4} - 5 + 4 x y^{3} z)$
Given polynomial is $12 x^{2} y^{3} z^{4} - 30 x y^{2} + 24 x^{2} y^{5} z$
Amongst all $6 x y^{2}$ is the common term from all.
So, taking $6 x y^{2}$ common, we get
$\Rightarrow 6 x y^{2} (2 x y z^{4} - 5 + 4 x y^{3} z)$

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