Question

1.Descompuneti in factori:

a) x²-2x+1
b) x³-x²+x-1

2.Aratati ca E(x)=1 pt∀ x∈R

E(x)=(x+1+2/x-1) x²-2x+1/x³-x²+x-1

Answer 1

a)
x^2-2x+1
Coeficientii:
A=1
B=-2
C=1
Suma: B=-2
Produs: A*C=1
divizorii lui 1=1;-1
1*1=1 1+1=2
(-1)*(-1)=1 (-1)+(-1)=-2(varianta potrivita)
x^2-2x+1=
(x^2-1x)-(1x-1)=
x*(x-1)-1*(x-1)=
(x-1)(x-1)=(x-1)^(1+1)=(x-1)^2
b)
x^3-x^2+x-1
Se formeaza doua grupe care se ,,intersecteaza"
Grupa 1:
x^3-x^2=x^2*(x-1)
Grupa 2:
x-1=1*(x-1)
x^2*(x-1)+1*(x-1)=(x^2+1)*(x-1)
2)
Verifica daca ai scris corect
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