Question

find the remainder when x raised to 11+1 is divided by (x+1)
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Answer 1

Answer:

The answer is 0

Step-by-step explanation:

$p(x) = {x}^{11} + 1 \\ divisor = x + 1 \\ x = - 1 \\ remainder = p( - 1) = ( - 1)^{11} + 1 \\ = - 1 + 1 \\ 0$

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Answer 2

Answer:

Remainder =0

Step-by-step explanation:

$\begin{array}{c|c|c|c|c|c|c|c|c|c|c|c|c}&x^{11}&x^{10}&x^9&x^8&x^7&x^6&x^5&x^4&x^3&x^2&x^1&1\\----&-&-&-&-&-&-&-&-&-&-&-&-\\&1&0&0&0&0&0&0&0&0&0&0&1\\x=-1&&-1&1&-1&1&-1&1&-1&1&-1&1&-1\\----&-&-&-&-&-&-&-&-&-&-&-&-\\&1&-1&1&-1&1&-1&1&-1&1&-1&1&0&\end{array}\\\\\\x^{11}+1=(x^{10}-x^9+x^8-x^7+x^6-x^5+x^4&-x^3+x^2-x^1+1)(x+1) + 0$