Subtract polynomials: $ \, \color{blue}{ x^3-4x^2+x+6 } \, $ , $ \, \color{orangered}{ 2x+5 }$.

$$ \left( \color{blue}{x^3-4x^2+x+6} \right) - \left( \color{orangered}{2x+5} \right) = x^3-4x^2-x+1 $$

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

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

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

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

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

$$ \begin{array}{lrrrr} & x^3 & -4x^2 & x & 6 \\ \color{red}{ - } & & & -2x & -5 \\ \hline & x^3 & -4x^2 & 3x & 11 \end{array} $$

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