Answer :
Final answer:
By using the remainder theorem and substituting -1 in place of x in the equation, we find that the remainder of the division x^{101} + 101 by x+1 is 100.
Explanation:
The problem here lies within a mathematics principle called polynomial division and the remainder theorem. Base on the remainder theorem, if a polynomial f(x) is divided by (x-a), the remainder is f(a). Therefore, if we want to find the remainder of x^{101} + 101 divided by x+1, we substitute -1 in place of x, as x+1 equals 0 when x equals -1. By substituting -1 into the equation, we get (-1)^{101} + 101 = -1 + 101 = 100. Hence the remainder is 100 (option 'a').
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Answer:
the correct answer is (a) 100.
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