Z⁸+Z⁴+1 solve factorize

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asked Dec 21, 2024 144k views

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Z⁸+Z⁴+1 solve factorize

Mathematics
college

Arturo Sbr asked

by Arturo Sbr

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Answer:

$\sf\\z^8+z^4+1\\\\=z^8+2z^4+1-z^4\\\\=(z^4+1)^2-(z^2)^2\\\\=(z^4+z^2+1)(z^4-z^2+1)\\\\=[z^4+2z^2+1-z^2](z^4-z^2+1)\\\\=[(z^2+1)^2-z^2](z^4-z^2+1)\\\\=(z^2+z+1)(z^2-z+1)(z^4-z^2+1)$

Russell Newquist answered Dec 24, 2024

by Russell Newquist

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