Step 1: Write second polynomial below the first one. Making sure like terms are lined up.
$$ \begin{array}{lrrr} & -4x^2 & & -7 \\ \color{blue}{ + } & 9x^2 & 4x & \\ \hline \end{array} $$Step 2: Combine like terms (add each column):
$$ \begin{array}{lrrr} & -4x^2 & & -7 \\ \color{blue}{ + } & 9x^2 & 4x & \\ \hline & 5x^2 & 4x & -7 \end{array} $$