Question

Aratati ca (x-5)^3-x+5=(x-4)(x-5)(x-6),pentru orice numar real x
Va rog !!!!!!

Answer 1

[tex](x-5)^3-x+5=(x-5)^3-1\cdot(x-5)=\\ =(x-5)[(x-5)^2-1]=(x-5)(x^2-10x+25-1)\\ =(x-5)(x^2-10x+24)=(x-5)(x^2-6x-4x+24)=\\ =(x-5)[x(x-6)-4(x-6)]=(x-5)(x-6)(x-4)=\\ =(x-4)(x-5)(x-6), \, \forall \, x \in \mathbb{R}[/tex]

Answer 2

 (x-5)³-x+5 =
= ( x-5)³ - (x-5) =
= (x-5)*((x-5)²-1) =
= (x-5)(x-5-1)(x-5+1) =
= (x-5)(x-6)(x-4) ( A )