Find the factors of $24 x^{2} y + 34 x y + 12 y$

2 y (2 x + 3) (3 x + 2)

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2 y (x + 2) (x + 3)

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2 y (4 x + 3) (3 x + 2)

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None of these

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Solution

The correct option is C $2 y (4 x + 3) (3 x + 2)$
$24 x^{2} y + 34 x y + 12 y$
$= 2 y [12 x^{2} + 17 x + 6]$
$= 2 y [12 x^{2} + 9 x + 8 x + 6]$
$= 2 y [3 x (4 x + 3) + 2 (4 x + 3)]$
$= 2 y (4 x + 4) (3 x + 2)$

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