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

$$ \begin{aligned} P(x) &= -3x^4+7x^2+x \\ Q(x) &= 8x^4+x^2+7x \\ \end{aligned} $$

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

$$ \begin{array}{lrrr} & -3x^4 & 7x^2 & x \\ \color{blue}{ + } & 8x^4 & x^2 & 7x \\ \hline \end{array} $$

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

$$ \begin{array}{lrrr} & -3x^4 & 7x^2 & x \\ \color{blue}{ + } & 8x^4 & x^2 & 7x \\ \hline & 5x^4 & 8x^2 & 8x \end{array} $$

Polynomial Operations Calculator