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Let m be a non-zero integer and n be a positive integer. Let R be the remainder obtained on dividing the polynomial xn + mn by (x – m). Then
  • a)
    R is a non-zero even integer
  • b)
    R = s2 for some integer s, if n is even
  • c)
    R = t2 for some integer s, if n is even
  • d)
    R = t3 for some integer t, if 3 divides n
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Let m be a non-zero integer and n be a positive integer. Let R be the ...
xn + mn = xn – mn + 2mn
For any positive integer ‘n’, xn – yn is divisible by x – y
The remainder when xn + mn is divided by (x – y), R = 2mn
∴ R is an even number
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Let m be a non-zero integer and n be a positive integer. Let R be the remainder obtained on dividing the polynomial xn+ mnby (x – m). Thena)R is a non-zero even integerb)R = s2for some integer s, if n is evenc)R = t2for some integer s, if n is evend)R = t3for some integer t, if 3 divides nCorrect answer is option 'A'. Can you explain this answer?
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