Subtract polynomials: $ \, \color{blue}{ x^{15}-1 } \, $ , $ \, \color{orangered}{ x^2+x }$.

$$ \left( \color{blue}{x^{15}-1} \right) - \left( \color{orangered}{x^2+x} \right) = x^{15}-x^2-x-1 $$

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

$$ \begin{array}{lrrrr} & x^{15} & & & -1 \\ \color{red}{ - } & & x^2 & x & \\ \hline \end{array} $$

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

$$ \begin{array}{lrrrr} & x^{15} & & & -1 \\ \color{red}{ - } & & -x^2 & -x & \\ \hline \end{array} $$

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

$$ \begin{array}{lrrrr} & x^{15} & & & -1 \\ \color{red}{ - } & & -x^2 & -x & \\ \hline & x^{15} & x^2 & x & -1 \end{array} $$

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