x^5-x 因式分解

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x^5-x 因式分解

x^5-x 因式分解
x^5-x 因式分解

x^5-x 因式分解
答:
x^5-x
=x(x^4-1)
=x(x^2-1)(x^2+1)
=x(x-1)(x+1)(x^2+1)

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

高中应该是实数域上分解=X(X^4-1)=X(X^2+1)(X^2-1)=X(X^2+1)(X+1)(X-1)

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