Subtract polynomials: $ \, \color{blue}{ 8x^3-10x^2+28x-16 } \, $ , $ \, \color{orangered}{ x-3 }$.

$$ \left( \color{blue}{8x^3-10x^2+28x-16} \right) - \left( \color{orangered}{x-3} \right) = 8x^3-10x^2+27x-13 $$

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

$$ \begin{array}{lrrrr} & 8x^3 & -10x^2 & 28x & -16 \\ \color{red}{ - } & & & x & -3 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrrr} & 8x^3 & -10x^2 & 28x & -16 \\ \color{red}{ - } & & & -x & 3 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrrr} & 8x^3 & -10x^2 & 28x & -16 \\ \color{red}{ - } & & & -x & 3 \\ \hline & 8x^3 & -10x^2 & 29x & -19 \end{array} $$

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