因式分解x^3+6x^2+11x+6

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因式分解x^3+6x^2+11x+6

因式分解x^3+6x^2+11x+6
因式分解x^3+6x^2+11x+6

因式分解x^3+6x^2+11x+6
(x^3+6x^2+11x+6)
=(x^3+3x^2)+(3x^2+11x+6)
=x^2(x+3)+(x+3)(3x+2)
=(x+3)(x^2+3x+2)
=(x+3)(x+2)(x+1)

原式=(x^3-x)+(6x^2+12x+6)=x*(x-1)*(x+1)+6(x+1)^2
=(x+1)*(x^2-x+6x+6)=(x+1)*(x+2)*(x+3)