Subtract polynomials: $ \, \color{blue}{ -x^5+12x^3+6x^2-23x+1 } \, $ , $ \, \color{orangered}{ x-2 }$.

$$ \left( \color{blue}{-x^5+12x^3+6x^2-23x+1} \right) - \left( \color{orangered}{x-2} \right) = -x^5+12x^3+6x^2-24x+3 $$

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

$$ \begin{array}{lrrrrr} & -x^5 & 12x^3 & 6x^2 & -23x & 1 \\ \color{red}{ - } & & & & x & -2 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrrrr} & -x^5 & 12x^3 & 6x^2 & -23x & 1 \\ \color{red}{ - } & & & & -x & 2 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrrrr} & -x^5 & 12x^3 & 6x^2 & -23x & 1 \\ \color{red}{ - } & & & & -x & 2 \\ \hline & -x^5 & 12x^3 & 6x^2 & -22x & -1 \end{array} $$

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