Add $ \, \color{blue}{ -x^2+4+1 } \, $ and $ \, \color{orangered}{ 3x^3-9-3x }$.

$$ \left( \color{blue}{-x^2+4+1} \right) + \left( \color{orangered}{3x^3-9-3x} \right) = 3x^3-x^2-3x-4 $$

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

$$ \begin{aligned} P(x) &= -x^2+5 \\ Q(x) &= 3x^3-3x-9 \\ \end{aligned} $$

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

$$ \begin{array}{lrrrr} & & -x^2 & & 5 \\ \color{blue}{ + } & 3x^3 & & -3x & -9 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrrr} & & -x^2 & & 5 \\ \color{blue}{ + } & 3x^3 & & -3x & -9 \\ \hline & 3x^3 & -x^2 & -3x & -4 \end{array} $$

Polynomial Operations Calculator