Subtract polynomials: $ \, \color{blue}{ -3x-2 } \, $ , $ \, \color{orangered}{ 6x^2-4+9 }$.

$$ \left( \color{blue}{-3x-2} \right) - \left( \color{orangered}{6x^2-4+9} \right) = -6x^2-3x-7 $$

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

$$ \begin{aligned} P(x) &= -3x-2 \\ Q(x) &= 6x^2+5 \\ \end{aligned} $$

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

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

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

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

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

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

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