Question

Se considera expresia E(x)=
$x^{3} - 2x^{2} - x + 2$
a) Descompuneti expresia in produs de factori primi
b) Calculati E(-3)
c) Aratati ca E($\sqrt{2}$)×E(-$\sqrt{2}$) apartine multimii nr. naturale

Answer 1

$\it E(x) = x^3-2x^2-x+2=x^2(x-2)-(x-2) =(x-2)(x^2-1)= \\ \\ =(x-2)(x-1)(x+1).$

b)

$\it E(-3) = (-3-2)(-3-1)(-3+1) = -5\cdot(-4)\cdot(-2)=-40$

c)

$\it E(\sqrt2) = (\sqrt2)^3-2(\sqrt2)^2-\sqrt2+2=2\sqrt2-2\cdot2-\sqrt2+2=\sqrt2-2 \\ \\ E(-\sqrt2) = (-\sqrt2)^3-2(-\sqrt2)^2-(-\sqrt2)+2= \\ \\ =-2\sqrt2-2\cdot2+\sqrt2+2=-\sqrt2-2=-(\sqrt2+2) \\ \\ E(\sqrt2)\cdot E(-\sqrt2) =- (\sqrt2-2)(\sqrt2+2)=-[(\sqrt2)^2-2^2] = \\ \\ =-(2-4)=-(-2)=2 \in\mathbb{N}$

Answer 2

Am anexat inca o rezolvare ---

--------------------------------------------