Question


Answer

x^{15}+x^{14}+x^{13}+\dots +x+1

=\dfrac{(x-1)(x^{15}+x^{14}+x^{13}+\dots +x+1)}{x-1}

=\dfrac{x^{16}-1}{x-1}

=\dfrac{(x^8+1)(x^8-1)}{x-1}

=\dfrac{(x^8+1)(x^4+1)(x^4-1)}{x-1}

=\dfrac{(x^8+1)(x^4+1)(x^2+1)(x^2-1)}{x-1}

=\dfrac{(x^8+1)(x^4+1)(x^2+1)(x+1)(x-1)}{x-1}

=(x^8+1)(x^4+1)(x^2+1)(x+1)

Steven Zheng posted 1 year ago

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