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The remainder when 3x3 - 2x2y - 13xy2 + 10y3 is divided by (x - 2y) is equal to

The remainder when 3x3 - 2x2y - 13xy2 + 10y3 is divided by (x - 2y) is equal to Correct Answer Zero 

According to remainder theorem, when any polynomial f(x) is divided by (x - a), the remainder obtained is given as f(a),

Let f(x) = 3x3 - 2x2y - 13xy2 + 10y3

Putting x = 2y,

⇒ f(2y) = 3(8y3) - 2y(4y2) - 13y2(2y) + 10y3 = 24y3 - 8y3 - 26y3 + 10y3 = 0

∴ Required remainder = 0

 

 

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