因式分解：x^4-7x^3+17x^2+7x+6

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因式分解：x^4-7x^3+17x^2+7x+6
是
x^4-7x^3+17x^2-17x+6

x^4-x^3 -6x^3+6x^2+11x^2-11x-6x+6
=x^3(x-1)-6x^2(x-1) +11x(x-1)-6(x-1)
=(x-1)(x^3-6x^2+11x-6)
=(x-1) [x^2(x-1)-5x(x-1)+6(x-1)]
=(x-1)^2(x^2-5x+6)
=(x-1)^2(x-2)(x-3)

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