求因式分解,x^3-11x^2+31x-21

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求因式分解,x^3-11x^2+31x-21
求因式分解,x^3-11x^2+31x-21

求因式分解,x^3-11x^2+31x-21
x^3-11x^2+31x-21
=x^3-7x^2-4x^2+28x+3x-21
=x^2(x-7)-4x(x-7)+3(x-7)
=(x-7)(x^2-4x+3)
=(x-7)(x-1)(x-3)

首先观察有一个解为x=1，所以
x^3-11x^2+31x-21=(x-1)(x^2-10x+21)=(x-1)(x-3)(x-7)

x^3-11x^2+31x-21=x³-x²-10x²+10x+21x-21=x²(x-1)-10x(x-1)+21(x-1)=(x-1)(x²-10x+21)
=(x-1)(x-3)(x-7)

x^3-11x^2+31x-21
=x^3-7x^2-4x^2+28x+3x-21
=x^2(x-7)-4x(x-7)+3(x-7)
=(x-7)(x^2-4x+3)
=(x-7)(x-1)(x-3) .

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