Add $ \, \color{blue}{ 12x^2+21x+9 } \, $ and $ \, \color{orangered}{ -18x^2-8-24x }$.

$$ \left( \color{blue}{12x^2+21x+9} \right) + \left( \color{orangered}{-18x^2-8-24x} \right) = -6x^2-3x+1 $$

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

$$ \begin{aligned} P(x) &= 12x^2+21x+9 \\ Q(x) &= -18x^2-24x-8 \\ \end{aligned} $$

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

$$ \begin{array}{lrrr} & 12x^2 & 21x & 9 \\ \color{blue}{ + } & -18x^2 & -24x & -8 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrr} & 12x^2 & 21x & 9 \\ \color{blue}{ + } & -18x^2 & -24x & -8 \\ \hline & -6x^2 & -3x & 1 \end{array} $$

Polynomial Operations Calculator