Add $ \, \color{blue}{ 5+7x^3+3x^2 } \, $ and $ \, \color{orangered}{ -12+5x+6x^2 }$.

$$ \left( \color{blue}{5+7x^3+3x^2} \right) + \left( \color{orangered}{-12+5x+6x^2} \right) = 7x^3+9x^2+5x-7 $$

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

$$ \begin{aligned} P(x) &= 7x^3+3x^2+5 \\ Q(x) &= 6x^2+5x-12 \\ \end{aligned} $$

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

$$ \begin{array}{lrrrr} & 7x^3 & 3x^2 & & 5 \\ \color{blue}{ + } & & 6x^2 & 5x & -12 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrrr} & 7x^3 & 3x^2 & & 5 \\ \color{blue}{ + } & & 6x^2 & 5x & -12 \\ \hline & 7x^3 & 9x^2 & 5x & -7 \end{array} $$

Polynomial Operations Calculator