Add $ \, \color{blue}{ -k-8k^3+5k^4+k^2 } \, $ and $ \, \color{orangered}{ -3k^3+6k^2+3k }$.

$$ \left( \color{blue}{-k-8k^3+5k^4+k^2} \right) + \left( \color{orangered}{-3k^3+6k^2+3k} \right) = 5k^4-11k^3+7k^2+2k $$

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

$$ \begin{aligned} P(x) &= 5k^4-8k^3+k^2-k \\ Q(x) &= -3k^3+6k^2+3k \\ \end{aligned} $$

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

$$ \begin{array}{lrrrr} & 5k^4 & -8k^3 & k^2 & -k \\ \color{blue}{ + } & & -3k^3 & 6k^2 & 3k \\ \hline \end{array} $$

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

$$ \begin{array}{lrrrr} & 5k^4 & -8k^3 & k^2 & -k \\ \color{blue}{ + } & & -3k^3 & 6k^2 & 3k \\ \hline & 5k^4 & -11k^3 & 7k^2 & 2k \end{array} $$

Polynomial Operations Calculator