Question

find the reminder when x51+51 is divided by (x+1)

Answer 1

You mean \(x^{51}+51\) divided by \(x+1\), right?

Answer 2

Aha.. the remainder theorem.

\( \color{Black}{\Rightarrow f(x) = x^{51} + 51 }\)

This is being divided by \(x - (-1)\)

Plug in -1 for x in f(x)

Answer 3

\( \color{Black}{\Rightarrow (-1)^{51} + 51}\)

^ remainder would be this

Answer 4

The odd powers of -1 are always -1.

\( \color{Black}{\Rightarrow -1 + 51}\)

\( \color{Black}{\Rightarrow 50}\)

Therefore, remainder is 50.