Question

Descompuneti in factori :
a) x^3-x^2-x+1
b) x^3+6x^2y+3xy^2
Vă rog mult e pentru teza please

Answer 1

a) $x^{3}-x^{2}-x+1=x^{2}(x-1)-(x-1)=(x^{2}-1)(x-1)=(x+1)(x-1)(x-1)=(x+1)(x-1)^{2}$
b) $x^{3}+6x^{2}y+3xy^{2}=x(x^{2}+6xy+3y^{2})=x(x(x+6y)+3y^{2})$

Answer 2

a) x³-x²-x+1 =x²(x-1)-(x-1)=(x-1)(x²-1)=(x-1)(x-1)(x+1)=(x-1)²(x+1)

b) x³+6x²y+3xy² =x(x²+6xy+3y²)=x(x²+6xy+3y²+6y²-6y²)=
=x(x²+6xy+9y²-6y²)=x[(x+3y)²-6y²]=x(x+3y-y√6)(x+3y+y√6)=
=x[x+y(3-√6)][x+y(3+√6)]