因式分解x的5方-x的4方+x的3方-x的2方+x-1,

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因式分解x的5方-x的4方+x的3方-x的2方+x-1,
因式分解x的5方-x的4方+x的3方-x的2方+x-1,

因式分解x的5方-x的4方+x的3方-x的2方+x-1,
原式=x^4(x-1)+x²(x-1)+(x-1)
=(x-1)(x^4+x²+1)
=(x-1)(x^4+2x²+1-x²)
=(x-1)[(x²+1)²-x²]
=(x-1)(x²+x+1)(x²-x+1)

x^5-x^4+x^3-x^2+x-1=x^3(x^2-x+1)-(x^2-x+1)=(x^3-1)(x^2-x+1)=(x-1)(x^2+x+1)(x^2-x+1)

x的5方-x的4方+x的3方-x的2方+x-1=x^4(x-1)+x^2(x-1)+(x-1)=(x^4+x^2+1)(x-1)=(x^4+2x^2+1-x^2)(x-1)=(x²+x+1)(x²-x+1)(x-1)

x的5方-x的4方+x的3方-x的2方+x-1
=x的4次方(x-1)+x²(x-1)+(x-1)
=(x-1)(x的4次方+x²+1)
=(x-1)(x的4次方+2x²+1-x²)
=(x-1)【(x²+1)²-x²】
=(x-1)(x²+x+1)(x²-x+1)