Subtract polynomials: $ \, \color{blue}{ x^3-2x^2-65x+18 } \, $ , $ \, \color{orangered}{ x-9 }$.

$$ \left( \color{blue}{x^3-2x^2-65x+18} \right) - \left( \color{orangered}{x-9} \right) = x^3-2x^2-66x+27 $$

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

$$ \begin{array}{lrrrr} & x^3 & -2x^2 & -65x & 18 \\ \color{red}{ - } & & & x & -9 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrrr} & x^3 & -2x^2 & -65x & 18 \\ \color{red}{ - } & & & -x & 9 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrrr} & x^3 & -2x^2 & -65x & 18 \\ \color{red}{ - } & & & -x & 9 \\ \hline & x^3 & -2x^2 & -64x & 9 \end{array} $$

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