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