Question

If x 51 + 51 is divisible by x + 1 then find the remainder

Answer 1

If x51 + 51 is divided by x + 1, then the remainder is
(a) 0       
(b) 1             
(c) 49             
(d) 50 
(d) Let p(x) = x51 + 51 . …(i)
When we divide p(x) by x+1, we get the remainder p(-1)
On putting x= -1 in Eq. (i), we get p(-1) = (-1)51 + 51
= -1 + 51 = 50
Hence, the remainder is 50. 

Answer 2

p(x)=x51+51
p(-1)=(-1)51+51
=-51+51
=0.
therefore ,x+1 is a factor of x51+51