Question

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

Answer 1

$(x-5)^3-x+5=(x-4)(x-5)(x-6) \\\\ x^3-5^3 -15x^2+75x-x+5=(x^2-5x-4x+20)(x-6) \\\\ x^3 -125 -15x^2+74x+5= (x^2-9x+20)(x-6) \\\\ x^3-15x^2+74x-120=x^3-6x^2-9x^2+54x+20x-120 \\\\ x^3-15x^2+74x-120=x^3-15x^2+74x-120 \ \ \ "A"$