Add $ \, \color{blue}{ 2x+3x^3+1 } \, $ and $ \, \color{orangered}{ 2+3x^2+x }$.

$$ \left( \color{blue}{2x+3x^3+1} \right) + \left( \color{orangered}{2+3x^2+x} \right) = 3x^3+3x^2+3x+3 $$

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

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

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

$$ \begin{array}{lrrrr} & 3x^3 & & 2x & 1 \\ \color{blue}{ + } & & 3x^2 & x & 2 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrrr} & 3x^3 & & 2x & 1 \\ \color{blue}{ + } & & 3x^2 & x & 2 \\ \hline & 3x^3 & 3x^2 & 3x & 3 \end{array} $$

Polynomial Operations Calculator