2个回答
展开全部
原式=x^4+x²+1+x(x-1)(x²+x+1)-x(x²+x+1)
=x(x-1)(x²+x+1)+x^4-x³-x+1
=x(x-1)(x²+x+1)+x³(x-1)-(x-1)
=(x-1)[x(x²+x+1)+(x-1)(x²+x+1)]
=(x-1)(x²+x+1)(2x-1)
解法2
原式=(x²+1+x)(x²+1-x)+x(x-2)(x²+x+1)
=(x²+x+1)(x²+1-x+x²-2x)
=(x²+x+1)(2x²-3x+1)
=(x²+x+1)(x-1)(2x-1)
=x(x-1)(x²+x+1)+x^4-x³-x+1
=x(x-1)(x²+x+1)+x³(x-1)-(x-1)
=(x-1)[x(x²+x+1)+(x-1)(x²+x+1)]
=(x-1)(x²+x+1)(2x-1)
解法2
原式=(x²+1+x)(x²+1-x)+x(x-2)(x²+x+1)
=(x²+x+1)(x²+1-x+x²-2x)
=(x²+x+1)(2x²-3x+1)
=(x²+x+1)(x-1)(2x-1)
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