Add $ \, \color{blue}{ -6x^4-3x^3+5+3x^2 } \, $ and $ \, \color{orangered}{ 8x^4+6x^3+4x^2 }$.

$$ \left( \color{blue}{-6x^4-3x^3+5+3x^2} \right) + \left( \color{orangered}{8x^4+6x^3+4x^2} \right) = 2x^4+3x^3+7x^2+5 $$

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

$$ \begin{aligned} P(x) &= -6x^4-3x^3+3x^2+5 \\ Q(x) &= 8x^4+6x^3+4x^2 \\ \end{aligned} $$

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

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

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

$$ \begin{array}{lrrrr} & -6x^4 & -3x^3 & 3x^2 & 5 \\ \color{blue}{ + } & 8x^4 & 6x^3 & 4x^2 & \\ \hline & 2x^4 & 3x^3 & 7x^2 & 5 \end{array} $$

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