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Binomial Theorem

If the polyno...

Question

If the polynomial $(x + 1)^{2015} - x^{2015} - 1$ is divided by $(x + x^{2} + x^{3})$ , then the remainder is

x^{2} - x

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x^{2} + x

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1

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0

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Solution

The correct option is D $0$
$Q (x + x^{2} + x^{3}) = x (1 + x + x^{2})$

$[(x + 1)^{2015} - x^{2015} - 1] = [x + x^{2} + x^{3}] q (x) + R (x)$

Put $x = 0$

$R (x) = 1 - 0 - 1 = 0$

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