Add $ \, \color{blue}{ 5x+9x^3-3x^5 } \, $ and $ \, \color{orangered}{ 8x^3+3x^5-2x }$.

$$ \left( \color{blue}{5x+9x^3-3x^5} \right) + \left( \color{orangered}{8x^3+3x^5-2x} \right) = 17x^3+3x $$

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

$$ \begin{aligned} P(x) &= -3x^5+9x^3+5x \\ Q(x) &= 3x^5+8x^3-2x \\ \end{aligned} $$

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

$$ \begin{array}{lrrr} & -3x^5 & 9x^3 & 5x \\ \color{blue}{ + } & 3x^5 & 8x^3 & -2x \\ \hline \end{array} $$

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

$$ \begin{array}{lrrr} & -3x^5 & 9x^3 & 5x \\ \color{blue}{ + } & 3x^5 & 8x^3 & -2x \\ \hline & & 17x^3 & 3x \end{array} $$

Polynomial Operations Calculator