Question

The remainder when x¹⁰¹ + 101 is divided by x + 1 is 

A) 1 

B) 100 

C) 101 

D) 0

Answer 1

Correct option is (B) 100

Let p(x) = \(x^{101}+101\)

\(\because\) When p(x) is divided by (x+1), it leaves remainder p(-1).

Now, p(-1) = \((-1)^{101}+101\) = -1+101 = 100

Hence, the remainder when \(x^{101}+101\) is divided by \((x+1)\) is 100.

Answer 2

Correct option is  A) 1