For n ∈ N , x n + 1 + ( x + 1 ) 2 n − 1 is divisible by

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MathematicsBinomial TheoremRemainder and Divisibility ProblemsHard2 minPYQ_2011

MathematicsHardsingle choice

For $n \in N, x^{n + 1} + (x + 1)^{2 n - 1}$ is divisible by

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Solution:

For $n = 1$ , we have; $x^{n + 1} + (x + 1)^{2 n - 1} = x^{2} + (x + 1) = x^{2} + x + 1,$ which is divisible by $x^{2} + x + 1$ For $n = 2$ , we have; $x^{n + 1} + (x + 1)^{2 n - 1}$ $= x^{3} + (x + 1)^{3} = (2 x + 1) (x^{2} + x + 1),$ which is divisible by $x^{2} + x + 1$ .

Stream:BITSATSubject:MathematicsTopic:Binomial TheoremSubtopic:Remainder and Divisibility Problems

⏱ 2mℹ️ Source: PYQ_2011

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