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Factorise : x^8 + x^4 + 1

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Factorise : \(x^8  + x^4  + 1\)

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\(x^8  + x^4  + 1\) = x8 + 2x4 + 1 -x4

= (x4 + 1)2 - (x2)2 = (x4 + 1 + x2) (x4 + 1 - x2)

= (x4 + 2x2 + 1 -x2)(x4 - x2 + 1)

= [(x2 + 1)2 - x2] (x4 - x2 + 1)

= (x2 + 1 + x)(x2 + 1 - x)(x4 - x2 + 1).

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