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

$$ \begin{aligned} P(x) &= 2x^3-x+5 \\ Q(x) &= -x^2+3x+1 \\ \end{aligned} $$

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

$$ \begin{array}{lrrrr} & 2x^3 & & -x & 5 \\ \color{red}{ - } & & -x^2 & 3x & 1 \\ \hline \end{array} $$

Step 3: Change ALL the signs in the second row.

$$ \begin{array}{lrrrr} & 2x^3 & & -x & 5 \\ \color{red}{ - } & & x^2 & -3x & -1 \\ \hline \end{array} $$

Step 4: Combine like terms (add each column):

$$ \begin{array}{lrrrr} & 2x^3 & & -x & 5 \\ \color{red}{ - } & & x^2 & -3x & -1 \\ \hline & 2x^3 & -x^2 & 2x & 6 \end{array} $$

Polynomial Operations Calculator