因式分解x^8+x^4+1

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因式分解x^8+x^4+1
因式分解x^8+x^4+1

因式分解x^8+x^4+1
x^8+x^4+1
=x^8+2x^4+1-x^4
=(x^4+1)^2-x^4
=(x^4+1+x^2)(x^4+1-x^2)
= (x^4+2x^2+1-x^2)(x^4-x^2+1)
=[(x^2+1)^2-x^2](x^4-x^2+1)
=(x^2+x+1)(x^2-x+1)(x^4-x^2+1)

x^8+x^4+1
=(x^4-1)((x^8+x^4+1)/(x^4-1)
=(x^12-1)/(x^4-1)
=(x^6-1)(x^6+1)/(x^4-1)
=(x^2-1)(x^4+x^2+1)(x^2+1)(x^4-x^2+1)/(x^4-1)
=(x^4+x^2+1)(x^4-x^2+1)
=(x^2+x+1)(x^2-x+1)(x^4-x^2+1)

x^8+x^4+1
=（x^8+2x^4+1 ）-x^4
=(x^4+1)^2-x^4
=(x^4+x^2+1)(x^4-x^2+1)
=[(x^2+1)^2-x^2](x^4-x^2+1)
=(x^2+x+1)(x^2-x+1)(x^4-x^2+1)

x^4(x^2 - i)(x^2 +i)

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