Prove the following

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.

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