Question

Scrieti sub forma de produs de trei factori care sa-l contina pe x expresia E(x)=x4-2x³+2x²-2x+1

Answer 1

E(x)=x⁴-2x³+2x²-2x+1=x⁴+2x²+1-2x³-2x=(x²+1)²-2x(x²+1)=(x²+1)(x²+1-2x)=(x²+1)(x²+2-1-2x)=(x²+1)(x²-1+2-2x)=(x²+1)[(x-1)(x+1)-2(x-1)]=(x²+1)(x-1)(x+1-2)=(x²+1)(x-1)(x-1)