Subtract polynomials: $ \, \color{blue}{ 4x^4-9x^3-7x^2-2x+25 } \, $ , $ \, \color{orangered}{ x+4 }$.

$$ \left( \color{blue}{4x^4-9x^3-7x^2-2x+25} \right) - \left( \color{orangered}{x+4} \right) = 4x^4-9x^3-7x^2-3x+21 $$

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

$$ \begin{array}{lrrrrr} & 4x^4 & -9x^3 & -7x^2 & -2x & 25 \\ \color{red}{ - } & & & & x & 4 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrrrr} & 4x^4 & -9x^3 & -7x^2 & -2x & 25 \\ \color{red}{ - } & & & & -x & -4 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrrrr} & 4x^4 & -9x^3 & -7x^2 & -2x & 25 \\ \color{red}{ - } & & & & -x & -4 \\ \hline & 4x^4 & -9x^3 & -7x^2 & -x & 29 \end{array} $$

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