stability function

I have an exercise which asks me to find polynomials $P$ and $Q$ with a degree $2$ that satisfy $$\exp(z)= \dfrac{P(z)}{Q(z)} + O(z^5)\ \text{for} \ z\to 0$$ My question is: Are they actually unique ($\rightarrow$ can something be actually unique if it is expressed with Landau?) or can I just take 2 polynomials of degree 2 for example in type of our known RK-stability-function which is the $$R(z)=\sum\limits_{k=0}^s \dfrac{z^k}{k!}$$

They are not unique if you allow multiplying both $P$ and $Q$ with a constant. I would make an ansatz $Q(z)=1+az+bz^2$, $P(z)=c+dz+ez^2$ and compare $\frac PQ$ with the Taylor expansion of $\exp(z)$. Note that we have five conditions for five unknowns $a,b,c,d,e$, so everything should work out nicely.