原式=x^4+5x-16+10
=(x^4-16)+(5x+10)
=(x^2+4)(x^-4)+5(x+2)
=(x^2+4)(x+2)(x-2)+5(x+2)=(x+2)((x^2+4)(x-2)+5)
=(x+2)(x^3-2x^2+4x-8+5)
=(x+2)(x^3-2x^2+4x-3)
=(x+2)(x^3-2x^2+x+3x-3)
=(x+2)(x(x^2-2x+1)+3(x-1))
=(x+2)(x(x-1)^2+3(x-1))
=(x+2)(x-1)(x(x-1)+3)
=(x+2)(x-1)(x^2-x+3)
在实系数范围内只能分解到这一步了,你满意吗?
(x-1)(x+2)(x^2-x+3)
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