Add $ \, \color{blue}{ 2x^3-5x+3x-9 } \, $ and $ \, \color{orangered}{ x^3+6x^2+11 }$.

$$ \left( \color{blue}{2x^3-5x+3x-9} \right) + \left( \color{orangered}{x^3+6x^2+11} \right) = 3x^3+6x^2-2x+2 $$

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

$$ \begin{aligned} P(x) &= 2x^3-2x-9 \\ Q(x) &= x^3+6x^2+11 \\ \end{aligned} $$

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

$$ \begin{array}{lrrrr} & 2x^3 & & -2x & -9 \\ \color{blue}{ + } & x^3 & 6x^2 & & 11 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrrr} & 2x^3 & & -2x & -9 \\ \color{blue}{ + } & x^3 & 6x^2 & & 11 \\ \hline & 3x^3 & 6x^2 & -2x & 2 \end{array} $$

Polynomial Operations Calculator