Well.. so many folks caught a cold
so many off that total, recovered,
keep in mind that, the folks who recovered
are just a fraction of the ones who were
sick
so... simply subtract the "recovered" polynomial,
from the "caugh cold" polynomial, namely
![\begin{cases} 8t-5t^2+t^3\impliedby &\textit{caught a cold}\\ \textendash\textendash\textendash\textendash\textendash\textendash\textendash\textendash\textendash\textendash\textendash\textendash\\ \cfrac{5-t^2+1}{5t^3}\impliedby &recovered \end{cases} \\ \quad \\\ [8t-5t^2+t^3]-\left[ \cfrac{5-t^2+1}{5t^3} \right]\implies \textit{still sick}](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7D%0A8t-5t%5E2%2Bt%5E3%5Cimpliedby%20%26%5Ctextit%7Bcaught%20a%20cold%7D%5C%5C%0A%5Ctextendash%5Ctextendash%5Ctextendash%5Ctextendash%5Ctextendash%5Ctextendash%5Ctextendash%5Ctextendash%5Ctextendash%5Ctextendash%5Ctextendash%5Ctextendash%5C%5C%0A%0A%5Ccfrac%7B5-t%5E2%2B1%7D%7B5t%5E3%7D%5Cimpliedby%20%26recovered%0A%5Cend%7Bcases%7D%0A%5C%5C%20%5Cquad%20%5C%5C%5C%0A%5B8t-5t%5E2%2Bt%5E3%5D-%5Cleft%5B%20%5Ccfrac%7B5-t%5E2%2B1%7D%7B5t%5E3%7D%20%5Cright%5D%5Cimplies%20%5Ctextit%7Bstill%20sick%7D)
so many off that total, recovered,
keep in mind that, the folks who recovered
are just a fraction of the ones who were
sick
so... simply subtract the "recovered" polynomial,
from the "caugh cold" polynomial, namely