Question
Add $ \, \color{blue}{ x^5+x^4+x^3+x^2+x } \, $ and $ \, \color{orangered}{ 2x^5-x^4+x^3-3x^2+x-1 }$.
Answer
$$ \left( \color{blue}{x^5+x^4+x^3+x^2+x} \right) + \left( \color{orangered}{2x^5-x^4+x^3-3x^2+x-1} \right) = 3x^5+2x^3-2x^2+2x-1 $$
Explanation
Step 1: Write second polynomial below the first one. Making sure like terms are lined up.
$$ \begin{array}{lrrrrrr} & x^5 & x^4 & x^3 & x^2 & x & \\ \color{blue}{ + } & 2x^5 & -x^4 & x^3 & -3x^2 & x & -1 \\ \hline \end{array} $$Step 2: Combine like terms (add each column):
$$ \begin{array}{lrrrrrr} & x^5 & x^4 & x^3 & x^2 & x & \\ \color{blue}{ + } & 2x^5 & -x^4 & x^3 & -3x^2 & x & -1 \\ \hline & 3x^5 & & 2x^3 & -2x^2 & 2x & -1 \end{array} $$This page was created using
Polynomial Operations Calculator