因式分解：x^4+2x^3-9x^2-2x+8

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因式分解：x^4+2x^3-9x^2-2x+8
因式分解：x^4+2x^3-9x^2-2x+8

因式分解：x^4+2x^3-9x^2-2x+8
x^4+2x^3-9x^2-2x+8
=x^4+2x^3-8x^2-x^2-2x+8
=x^2*(x^2+2x-8)-(x^2+2x-8)
=(x^2-1)(x^2+2x-8)
=(x+1)(x-1)(x-2)(x+4)

x^4-9x^2+8+2x^3-2x
=(x^-1)(x^-8)+2x^3-2x
=2x(x^2-1)+(x^2-1)(x^2-8)
=(x^2-1)(2x+x^2-8)
=(x^-1)(x-4)(x+2)
=(x+1)(x-1)(x-4)(x+2)

x^4+2x^3-9x^2-2x+8=x^4-2x^3+4x^3-8x^2-x^2+2x-4x+8
=x^3(x-2)+4x^2(x-2)-x(x-2)-4(x-2)
=(x-2)(x^3+4x^2-x-4)=(x-2)(x^3-x^2+5x^2-5x+4x-4)
=(x-2)[x^2(x-1)+5x(x-1)+4(x-1)]
=(x-2)(x-1)(x^2+5x+4)=(x-2)(x-1)(x+1)(x+4)

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