Step 1: Write second polynomial below the first one. Making sure like terms are lined up.
$$ \begin{array}{lrrrrr} & & & & x & -8 \\ \color{blue}{ + } & 4x^5 & -31x^4 & -66x^2 & 16x & 3 \\ \hline \end{array} $$Step 2: Combine like terms (add each column):
$$ \begin{array}{lrrrrr} & & & & x & -8 \\ \color{blue}{ + } & 4x^5 & -31x^4 & -66x^2 & 16x & 3 \\ \hline & 4x^5 & -31x^4 & -66x^2 & 17x & -5 \end{array} $$