If $2 x + k y + z$ is a factor of $9 y^{2} - z^{2} - 2 x z + 6 x y$ , then the value of k is equal to

-3

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-1

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Solution

The correct option is D 3
$9 y^{2} - z^{2} - 2 x z + 6 x y$ has coefficient of $z^{2} = - 1$ and coefficient of $x^{2} = 0$ and coefficient of $y^{2} = 9$
hence, $(2 x + k y + z) (- z + \frac{9}{k} y) = 9 y^{2} - z^{2} - 2 x z + 6 x y$
so from coefficient of $x y$ from both sides we can deduce that $k = 3$

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