If $3 x^{3} - 2 x^{2} y - 13 x y^{2} + 10 y^{3}$ is divided by $x - 2 y$ , then what is the remainder?

0

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x

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y + 5

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x - 3

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Solution

The correct option is B $0$
$x - 2 y | ¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ 3 x^{3} - 2 x^{2} y - 13 x y^{2} + 10 y^{3} | 3 x^{2} + 4 x y - 5 y^{2}$
$3 x^{3} - - 6 x^{2} y + - --------- -$
$4 x^{2} y - 13 x y^{2} + 10 y^{3}$
$4 x^{2} y - - 8 x y^{2} + - ----------- -$
$- 5 x y^{2} + 10 y^{3}$
$- 5 x y^{2} + + 10 y^{3} - - ------------- -$
$0 -$
Therefore, remainder $= 0$

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