Subtract polynomials: $ \, \color{blue}{ -12x+x-6 } \, $ , $ \, \color{orangered}{ 8x-6x-4 }$.

$$ \left( \color{blue}{-12x+x-6} \right) - \left( \color{orangered}{8x-6x-4} \right) = -13x-2 $$

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

$$ \begin{aligned} P(x) &= -11x-6 \\ Q(x) &= 2x-4 \\ \end{aligned} $$

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

$$ \begin{array}{lrr} & -11x & -6 \\ \color{red}{ - } & 2x & -4 \\ \hline \end{array} $$

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

$$ \begin{array}{lrr} & -11x & -6 \\ \color{red}{ - } & -2x & 4 \\ \hline \end{array} $$

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

$$ \begin{array}{lrr} & -11x & -6 \\ \color{red}{ - } & -2x & 4 \\ \hline & -9x & -10 \end{array} $$

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