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

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

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

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

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

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

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

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

Polynomial Operations Calculator