Add $ \, \color{blue}{ 6+7q^3-3q^4 } \, $ and $ \, \color{orangered}{ 9q^4+2q^2-4 }$.

$$ \left( \color{blue}{6+7q^3-3q^4} \right) + \left( \color{orangered}{9q^4+2q^2-4} \right) = 6q^4+7q^3+2q^2+2 $$

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

$$ \begin{aligned} P(x) &= -3q^4+7q^3+6 \\ Q(x) &= 9q^4+2q^2-4 \\ \end{aligned} $$

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

$$ \begin{array}{lrrrr} & -3q^4 & 7q^3 & & 6 \\ \color{blue}{ + } & 9q^4 & & 2q^2 & -4 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrrr} & -3q^4 & 7q^3 & & 6 \\ \color{blue}{ + } & 9q^4 & & 2q^2 & -4 \\ \hline & 6q^4 & 7q^3 & 2q^2 & 2 \end{array} $$

Polynomial Operations Calculator