Which of the following is a factor of $3 x^{3} - 2 x^{2} y - 13 x y^{2} + 10 y^{3}$

x + y

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x - 2 y

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x + 2 y

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x - y

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Solution

The correct option is B $x - 2 y$
Let, $p (x) = 3 x^{3} - 2 x^{2} y - 13 x y^{2} + 10 y^{3}$
put $x = 2 y$ in $p (x)$
$p (2 y) = 3 {(2 y)}^{3} - 2 {(2 y)}^{2} y - 13 (2 y) {(y)}^{2} + 10 {(y)}^{3}$
$= 24 y^{3} - 8 y^{3} - 26 y^{3} + 10 y^{3}$
$= 34 y^{3} - 34 y^{3} = 0$
Since, $p (2 y) = 0$
$∴ x - 2 y$ is a factor of $p (x)$
Option B is correct.

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