因式分解x的四次方减去4x平方减去X加上2

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因式分解x的四次方减去4x平方减去X加上2

因式分解x的四次方减去4x平方减去X加上2
因式分解x的四次方减去4x平方减去X加上2

因式分解x的四次方减去4x平方减去X加上2
x^4-4x^2-x+2
=x^2(x^2-4)-(x-2)
=x^2(x+2)(x-2)-(x-2)
=(x-2)(x^3+2x^2-1)
=(x-2)(x+1)(x^2+x-1)

x^4-4x²-x+2
=x²(x²-4)-(x-2)
=x²(x+2)(x-2)-(x-2)
=(x³+2x²-1)(x-2)
=(x-2)[x³+x²+x²-1)
=(x-2)[x²(x+1)+(x+1)(x-1)]
=(x-2)(x+1)(x²+x-1)

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