Question

Find the remainder when x51 + 51 is divided by x+ 1.

Answer 1

Let P(x) = x51 + 51 be the given polynomial

If (x + 1) is a factor of P(x) => P(-1) = 0

but P(-1) = (-1)51 + 51 = -1 + 51 = 50.

So, the remainder is 50.