Step 1: First we have to write polynomials in descending order.

$$ \begin{aligned} P(x) &= x+1 \\ Q(x) &= 7x^2+10x+8 \\ \end{aligned} $$

Step 2: Write second polynomial below the first one. Making sure like terms are lined up.

$$ \begin{array}{lrrr} & & x & 1 \\ \color{blue}{ + } & 7x^2 & 10x & 8 \\ \hline \end{array} $$

Step 3: Combine like terms (add each column):

$$ \begin{array}{lrrr} & & x & 1 \\ \color{blue}{ + } & 7x^2 & 10x & 8 \\ \hline & 7x^2 & 11x & 9 \end{array} $$

Polynomial Operations Calculator