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(x-5)³-x+5=(x-4)(x-5)(x-6),pentru orice numar real x

Răspuns :

[tex](x-5)^3-x+5=(x-4)*(x-5)*(x-6)\\\\ x^3-5^3-15x^+75x-x+5=(x^2-5x-4x+20)*(x-6)\\\\ x^3-125-15x^2+74x+5=(x^2-9x+20)*(x-6)\\\\ x^3-15x^2+74x-120=x^3-6x^2+54x-20x-120\\\\ x^3-15x^2+74x-120=x^3-15x^2+74x-120 \ \ \ ``A``[/tex]