Subtract polynomials: $ \, \color{blue}{ -8x+7x-8 } \, $ , $ \, \color{orangered}{ 1820x+3x+9 }$.

$$ \left( \color{blue}{-8x+7x-8} \right) - \left( \color{orangered}{1820x+3x+9} \right) = -1824x-17 $$

Step 1: First we have to write polynomials in descending order.

$$ \begin{aligned} P(x) &= -x-8 \\ Q(x) &= 1823x+9 \\ \end{aligned} $$

Step 2: Write second polynomial below the first one. Making sure like terms are lined up.

$$ \begin{array}{lrr} & -x & -8 \\ \color{red}{ - } & 1823x & 9 \\ \hline \end{array} $$

Step 3: Change ALL the signs in the second row.

$$ \begin{array}{lrr} & -x & -8 \\ \color{red}{ - } & -1823x & -9 \\ \hline \end{array} $$

Step 4: Combine like terms (add each column):

$$ \begin{array}{lrr} & -x & -8 \\ \color{red}{ - } & -1823x & -9 \\ \hline & 1822x & 1 \end{array} $$

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