Question

arătați că x(x-2)la a doua+2(3x la a doua-1)-5x=(x-1)(x+1)(x+2),pentru orice XER​

Answer 1

$x(x-2)^2+2(3x^2-1)-5x=x(x^2-4x+4)+6x^2-2-5x = \\ \\ =x^3-4x^2+4x+6x^2-5x-2 = \\ \\ =x^3+2x^2-x-2 = x^2(x+2)-(x+2) = (x+2)(x^2-1) = \\ \\ = (x+2)(x-1)(x+1) = (x-1)(x+1)(x+2)$