Subtract polynomials: $ \, \color{blue}{ -2x^3+3x^2-8x-12 } \, $ , $ \, \color{orangered}{ 2x+3 }$.

$$ \left( \color{blue}{-2x^3+3x^2-8x-12} \right) - \left( \color{orangered}{2x+3} \right) = -2x^3+3x^2-10x-15 $$

Step 1: Write second polynomial below the first one. Making sure like terms are lined up.

$$ \begin{array}{lrrrr} & -2x^3 & 3x^2 & -8x & -12 \\ \color{red}{ - } & & & 2x & 3 \\ \hline \end{array} $$

Step 2: Change ALL the signs in the second row.

$$ \begin{array}{lrrrr} & -2x^3 & 3x^2 & -8x & -12 \\ \color{red}{ - } & & & -2x & -3 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrrr} & -2x^3 & 3x^2 & -8x & -12 \\ \color{red}{ - } & & & -2x & -3 \\ \hline & -2x^3 & 3x^2 & -6x & -9 \end{array} $$

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