2016 · Q11
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
Elementary MathematicsAlgebra
- AR is a non-zero even integer
- BR is odd, if m is odd
- CR = s² for some integer s, if n is even
- DR = t³ for some integer f, if 3 divides n
Explanation
By the remainder theorem, the remainder of xⁿ+mⁿ upon division by (x−m) is mⁿ+mⁿ = 2mⁿ. Since m is a non-zero integer, R = 2mⁿ is non-zero and even, so option A holds. It cannot be odd (option B), and the factor 2 stops it from being a perfect square or cube in general, ruling out C and D.