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# polynomial division

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Find the remainder when x^15 + 1 is divided by x-1.

Sep 30, 2020

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Find the remainder when x^15 + 1 is divided by x-1.

Hello Guest!

$$(x^{15}$$ $$+1)$$    :  $$(x-1)$$ $$=x^{14}+x^{13}+…+x^2+x$$$$+\large \frac{x+1}{x-1}$$

$$\underline{x^{15}-x^{14}}$$

$$x^{14}$$

$$\underline{x^{14}-x^{13}}$$                                                            $$\frac{x+1}{x-1}=1+\frac{2}{x-1}$$

$$x^{13 }$$

.... $$\underline{x^2-x}$$

$$x\color{red}+1$$

!

Oct 1, 2020