If $x^{501} + 501$ is divided by $x + 1$ , find the remainder.

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Solution

$\begin{matrix} x^{501} + 501 \to (i) x + 1 = 0 x = - 1 p u t i n e q . (i) {(- 1)}^{501} + 501 - 1 + 501 = 500 \end{matrix}$

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If x501+501 is divided by x+1, find the remainder.

x501+501→(i)x+1=0x=−1putineq.(i)(−1)501+501−1+501=500

If $x^{501} + 501$ is divided by $x + 1$ , find the remainder.

$\begin{matrix} x^{501} + 501 \to (i) x + 1 = 0 x = - 1 p u t i n e q . (i) {(- 1)}^{501} + 501 - 1 + 501 = 500 \end{matrix}$