Răspuns:
Explicație pas cu pas:
E(x)=x⁴+x²+1
F(x)=x²-x+1
G(x)=x²+x+1
a) F(n+2)-G(n+1)=(n+2)²-(n+2)+1-[(n+1)²+(n+1)+1]=(n+2)²-n-2+1-(n+1)²-n-1-1=(n+2)²-(n+1)²-2n-3=[(n+2)-(n+1)]x[(n+2)+(n+1)]-2n-3=(n+2-n-1)(n+2+n+1)-3=1·(2n+3)-2n-3=2n+3-2n-3=0.
b) x⁴+x²+1=x⁴+2x²+1-x²=(x²+1)²-x²=(x²+1-x)(x²+1+x)=(x²-x+1)·(x²+x+1)=F(x)·G(x)
