Question

find the remainder when the polynomial p( x) =x ^61 + 61 is divided by x-1

Answer 1

122 is the remainder and answer

Answer 2

$p(x) = {x}^{61} + 61 \\ we \: know \: that \: if \: we \: divide \: any \\ polynomial \: by \: (x - a) \\ \: then \: its \: remainder \: = p(a) \\ hence \:when \: p(x) \: is \: divided \: by \: (x - 1) \: its \\ \: remainder \: = p(1) = {1}^{61} + 62 \\= 1 + 61 = 62$