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$x (x^{n - 1} - {na}^{n - 1}) + a^{n} (n - 1)$ is divisible by $(x - a)^{2}$ for

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n>1

n>2

all n∈N

None of these

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detailed solution

Correct option is C

Check the options. The condition is satisfied for all n ∈ N.

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xxn−1−nan−1+an(n−1) is divisible by (x−a)2 for

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$x (x^{n - 1} - {na}^{n - 1}) + a^{n} (n - 1)$ is divisible by $(x - a)^{2}$ for