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Question
If x51 + 51 is divided by x + 1, the remainder is ______.
Options
0
1
49
50
Solution
If x51 + 51 is divided by x + 1, the remainder is 50.
Explanation:
Let f(x) = x51 + 51
We know that when f(x) is divided by x + a, then the remainder is f(–a).
So, remainder is
f(–1) = (–1)51 + 51
= –1 + 51
= 50
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