Question

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

(a) 0

(b)

(c) 49

(d) 50

Answer 1

(d) 50 

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.