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Q.

If x51 + 51 is divided by x + 1, Then the remainder is  


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a

0 

b

1  

c

49  

d

50  

answer is D.

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Detailed Solution

Concept- We are going to apply the remainder theorem concept.
Remainder theorem- If any polynomial f(x) is divided by f(x-h) , then the remainder will be f (h)
Here given polynomial is x51+51 and divided by  x+1
Using the theorem- Remainder f(-1)  since the divisor is x+1
Therefore, we can write it as
f(x) =x51+51 f(-1) =(-1) 51+51 f(-1) =-1+51 ∴f(-1) =50 
So, the remainder is 50.
Hence, the correct option is 4) 50
 
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