Add $ \, \color{blue}{ 5x^2+x-10 } \, $ and $ \, \color{orangered}{ -12-x+3x^2 }$.

$$ \left( \color{blue}{5x^2+x-10} \right) + \left( \color{orangered}{-12-x+3x^2} \right) = 8x^2-22 $$

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

$$ \begin{aligned} P(x) &= 5x^2+x-10 \\ Q(x) &= 3x^2-x-12 \\ \end{aligned} $$

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

$$ \begin{array}{lrrr} & 5x^2 & x & -10 \\ \color{blue}{ + } & 3x^2 & -x & -12 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrr} & 5x^2 & x & -10 \\ \color{blue}{ + } & 3x^2 & -x & -12 \\ \hline & 8x^2 & & -22 \end{array} $$

Polynomial Operations Calculator