Step 1: Write second polynomial below the first one. Making sure like terms are lined up.
$$ \begin{array}{lrrr} & 12x^2 & & -7 \\ \color{blue}{ + } & x^2 & -5x & -3 \\ \hline \end{array} $$Step 2: Combine like terms (add each column):
$$ \begin{array}{lrrr} & 12x^2 & & -7 \\ \color{blue}{ + } & x^2 & -5x & -3 \\ \hline & 13x^2 & -5x & -10 \end{array} $$