Question

the remainder when is x⁵⁰⁵¹+1 divided by x+1 is​

Answer 1

p(x) = x^5051 + 1

g(x) = x + 1

p(x) is to be divided by g(x)

Thus, g(x) = x + 1= 0

           x = -1

Putting the value of x = -1 in p(x),

p(-1) = (-1)^5051 + 1

       = -1 + 1          [ (-1)^any odd integer = -1]

       = 0

Thus remainder = 0 when x^5051 + 1 is divided by x + 1

Answer 2

first ,Find the Zero of linear polynomial

then, apply Remainder theorem