Question

Find the remainder when x^{​​​​​​51} + 51 is divided by (1) x+1 (2) x-1

Answer 1

(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.

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=52.
Hence the remainder is 52.