The expression in the denominator is [tex]\displaystyle{ x^2-2x-8[/tex].
We can use this expression by completing the square, and the difference of squares as follows:
[tex]\displaystyle{ x^2-2x-8=(x^2-2x+1)-9=(x-1)^2-3^2[/tex]
[tex]=(x-1-3)(x-1+3)=(x-4)(x+2)[/tex].
So, the zeros of the polynomial [tex]\displaystyle{ P(x)=x^2-2x-8[/tex] are x=4 and x=-2.
Thus, the asymptotes are the lines x=-2, and x=4.
Answer: D
