Question

find the remainder when x^51+51 is divided by x+1 (50)

Answer 1

$p(x) = x {}^{51} + 51 \\ g(x) = x + 1 \\ by \: remainder \: theorem \\ x + 1 = 0 \\ x = - 1 \\ so \: \: remainder = p( - 1) \\ = ( - 1) {}^{51} + 51$
Since, the power of (-1) is odd number so it is a negative integer.
$= ( - 1) {}^{51} + 51 \\ = - 1 + 51 \\ = 50$