Add $ \, \color{blue}{ 8x^2-15x-19 } \, $ and $ \, \color{orangered}{ 7-7x+2x^2 }$.

$$ \left( \color{blue}{8x^2-15x-19} \right) + \left( \color{orangered}{7-7x+2x^2} \right) = 10x^2-22x-12 $$

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

$$ \begin{aligned} P(x) &= 8x^2-15x-19 \\ Q(x) &= 2x^2-7x+7 \\ \end{aligned} $$

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

$$ \begin{array}{lrrr} & 8x^2 & -15x & -19 \\ \color{blue}{ + } & 2x^2 & -7x & 7 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrr} & 8x^2 & -15x & -19 \\ \color{blue}{ + } & 2x^2 & -7x & 7 \\ \hline & 10x^2 & -22x & -12 \end{array} $$

Polynomial Operations Calculator