Question

哪位兄台知道因式分解x^4-2x^2+x，详细点哈O(∩_∩)O谢谢

还有我今年升高中，是不是高中数学都这么变态T.T

Answer 1

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

Answer 2

竟然不知道先把x提出来
x^4-2x^2+x
=x(x^3-2x+1)
=x[(x^3-x^2)+(x^2-2x+1)]
=x[x^2(x-1)+(x-1)^2]
=x(x-1)(x^2+x-1)

Answer 3

x^4-2x^2+x
=x(x^3-2x+1)
=x[(x^3-x^2)+(x^2-2x+1)]
=x[x^2(x-1)+(x-1)^2]
=x(x-1)(x^2+x-1)