Question

Se considera expresia E(x)=x³-2x²-x+2
a)Descompuneti expresia in produs de factori primi
b)Calculati E(-3).
Multumesc!!!

Answer 1

$E_(_x_)=x^3-2x^2-x+2 \\ a).x^3-2x^2-x+2=x^2(x-2)-(x-2)=(x-2)(x^2-1)= \\ =(x-2)(x-1)(x+1) \\ b).E_(_-_3_)=? \\ E_(_-_3_)=(-3)^3-2*(-3)^2-(-3)+2=-27-2*9-(-3)+2= \\ =-27-18-(-3)+2=-45-(-3)+2=-42+2=-40 \\ E_(_-_3_)=-40$

Answer 2

    
[tex]a) \\ E(x)=x^3-2x^2-x+2= \\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~unde:~~-2x^2 =-x^2-x^2 ~~~s~~i~-x=x-2x \\ =x^3-x^2-x^2+x-2x+2= \\ x^2(x-1) -x(x-1)-2(x-1)= \\ =(x-1)(x^2-x-2)= ~~~~unde:~~~-x= x-2x \\ =(x-1)(x^2+x-2x-2)= \\ =(x-1)[x(x+1)-2)x+1)] =\boxed{(x-1)(x+1)(x-2) } \\ \\ b) \\ E(-3)=3^3-2\cdot(-3)^2 -(-3)+2=-27-2\cdot9+3+2=\boxed{-40}[/tex]