Add $ \, \color{blue}{ 3x^4-8x } \, $ and $ \, \color{orangered}{ 2x-4x^4 }$.

$$ \left( \color{blue}{3x^4-8x} \right) + \left( \color{orangered}{2x-4x^4} \right) = -x^4-6x $$

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

$$ \begin{aligned} P(x) &= 3x^4-8x \\ Q(x) &= -4x^4+2x \\ \end{aligned} $$

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

$$ \begin{array}{lrr} & 3x^4 & -8x \\ \color{blue}{ + } & -4x^4 & 2x \\ \hline \end{array} $$

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

$$ \begin{array}{lrr} & 3x^4 & -8x \\ \color{blue}{ + } & -4x^4 & 2x \\ \hline & -x^4 & -6x \end{array} $$

Polynomial Operations Calculator