Question:
If $x^{51}+51$ is divided by $x+1$, then the remainder is
(a) 0
(b) 1
(c) 49
(d) 50
Solution:
(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.