Add $ \, \color{blue}{ 3-x^2-2x^3 } \, $ and $ \, \color{orangered}{ 6+3x^3+7x^2 }$.

$$ \left( \color{blue}{3-x^2-2x^3} \right) + \left( \color{orangered}{6+3x^3+7x^2} \right) = x^3+6x^2+9 $$

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

$$ \begin{aligned} P(x) &= -2x^3-x^2+3 \\ Q(x) &= 3x^3+7x^2+6 \\ \end{aligned} $$

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

$$ \begin{array}{lrrr} & -2x^3 & -x^2 & 3 \\ \color{blue}{ + } & 3x^3 & 7x^2 & 6 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrr} & -2x^3 & -x^2 & 3 \\ \color{blue}{ + } & 3x^3 & 7x^2 & 6 \\ \hline & x^3 & 6x^2 & 9 \end{array} $$

Polynomial Operations Calculator