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Quantitative Aptitude

Divisibility Rule for Powers of 2 & 5

The remainder...

Question

The remainder when $81 x^{1857} + 81$ is divided by $x + 1$ is ______________

A

0

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B

1`

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C

162

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D

81

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Solution

The correct option is A 0
$\frac{81 (x^{1857} + 1)}{(x + 1)} \Rightarrow \frac{81 ((x + 1 - 1)^{1857} + 1)}{x + 1}$
$\Rightarrow \frac{81 (d i v i s i b l e) - 1 + 1}{x + 1}$
$\Rightarrow 0$

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