Add $ \, \color{blue}{ -2x^2+10x^4+x^3 } \, $ and $ \, \color{orangered}{ 4x^3+3x^4+8x^2 }$.

$$ \left( \color{blue}{-2x^2+10x^4+x^3} \right) + \left( \color{orangered}{4x^3+3x^4+8x^2} \right) = 13x^4+5x^3+6x^2 $$

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

$$ \begin{aligned} P(x) &= 10x^4+x^3-2x^2 \\ Q(x) &= 3x^4+4x^3+8x^2 \\ \end{aligned} $$

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

$$ \begin{array}{lrrr} & 10x^4 & x^3 & -2x^2 \\ \color{blue}{ + } & 3x^4 & 4x^3 & 8x^2 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrr} & 10x^4 & x^3 & -2x^2 \\ \color{blue}{ + } & 3x^4 & 4x^3 & 8x^2 \\ \hline & 13x^4 & 5x^3 & 6x^2 \end{array} $$

Polynomial Operations Calculator