Subtract polynomials: $ \, \color{blue}{ 5x+x } \, $ , $ \, \color{orangered}{ 2x+5 }$.

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

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

$$ \begin{aligned} P(x) &= 6x \\ Q(x) &= 2x+5 \\ \end{aligned} $$

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

$$ \begin{array}{lrr} & 6x & \\ \color{red}{ - } & 2x & 5 \\ \hline \end{array} $$

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

$$ \begin{array}{lrr} & 6x & \\ \color{red}{ - } & -2x & -5 \\ \hline \end{array} $$

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

$$ \begin{array}{lrr} & 6x & \\ \color{red}{ - } & -2x & -5 \\ \hline & 8x & 5 \end{array} $$

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