3. Among the functions $f(x)=\frac{a x^{2}+b x+8}{(x+c)^{2}}$, choose the one that has the domain

$\mathrm{D}_{f}=(-\infty, 1) \cup(1, \infty)$, a zero at 2, and an asymptote $y=0$.
3. From the domain, we read that the pole is $x=1$, so we write the equation $(1+c)^{2}=0$.
We calculate $c=-1$. From the equation of the asymptote, we read that the degree of the numerator is less than the degree of the denominator, so $a=0$. We consider that the number 2 is a zero of the function: $a \cdot 0+2 b+8=0$, from which we calculate $b=-4$. The function is $f(x)=\frac{-4 x+8}{(x+1)^{2}}$.
Using the pole $x=1 \mathrm{v}(1+c)^{2}=0$ ..... 1 point
Calculation $c=-1$ ..... 1 point
Using the asymptote ..... 1 point
Writing the equation $2 b+8=0$ ..... 1 point
Calculation $b=-4$ ..... 1 point
Writing the function $f(x)=\frac{-4 x+8}{(x+1)^{2}}$. ..... 1 point