Resposta :
Dx : (x²+1) = x²-6 e r = x+6
Dx = (x²-6).(x²+1) + x+6
Dx = x^4+x²-6x²-6+x+6
Dx = x^4-5x²+x
Dx = (x²-6).(x²+1) + x+6
Dx = x^4+x²-6x²-6+x+6
Dx = x^4-5x²+x
Basta fazer:
[tex]D(x)=(x^2+1).(x^2-6)+x+6 \\ \\ D(x)=x^4-6x^2+x^2-6+x+6 \\ \\ \boxed{D(x)=x^4-5x^2+x}[/tex]
[tex]D(x)=(x^2+1).(x^2-6)+x+6 \\ \\ D(x)=x^4-6x^2+x^2-6+x+6 \\ \\ \boxed{D(x)=x^4-5x^2+x}[/tex]