x^3+6x^2+11x+6的解法,要详细的步骤,麻烦了

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x^3+6x^2+11x+6的解法,要详细的步骤,麻烦了

x^3+6x^2+11x+6的解法,要详细的步骤,麻烦了
x^3+6x^2+11x+6的解法,要详细的步骤,麻烦了

x^3+6x^2+11x+6的解法,要详细的步骤,麻烦了
x^3+6x^2+11x+6
=(x^3+2x^2)+(4x^2+8x)+(3x+6)
=x^2(x+2)+4x(x+2)+3(x+2)
=(x^2+4x+3)(x+2)
=(x+1)(x+3)(x+2)

原式

=(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)

x³+6x²+11x+6
=(x³+x²)+(5x²+5x)+(6x+6)
=x²(x+1)+5x(x+1)+6(x+1)
=(x+1)(x²+5x+6)
=(x+1)(x+2)(x+3).

x^3+6x^2+11x+6
=x^3-x+6x^2+12x+6
=x(x^2-1)+6(x^2+2x+1)
=x(x+1)(x-1)+6(x+1)^2
=(x+1)[x(x-1)+6(x+1)]
=(x+1)(x^2+5x+6)
=(x+1)(x+2)(x+3)
剩下的会解了吧

x^3+611x+6+11x+6=x^3+x^2+5x^2+11x+6=x^2(x+1)+(5x^2+11x+6)
=x^2(x+1)+(x+1)(5x+6)
=(x+1)(x^2+5x+6)
=(x+1)(x+2)(x+3)