Subtract polynomials: $ \, \color{blue}{ 2x^3+4x^2-5x-3 } \, $ , $ \, \color{orangered}{ -x^3+5x^2-4 }$.

$$ \left( \color{blue}{2x^3+4x^2-5x-3} \right) - \left( \color{orangered}{-x^3+5x^2-4} \right) = 3x^3-x^2-5x+1 $$

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

$$ \begin{array}{lrrrr} & 2x^3 & 4x^2 & -5x & -3 \\ \color{red}{ - } & -x^3 & 5x^2 & & -4 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrrr} & 2x^3 & 4x^2 & -5x & -3 \\ \color{red}{ - } & x^3 & -5x^2 & & 4 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrrr} & 2x^3 & 4x^2 & -5x & -3 \\ \color{red}{ - } & x^3 & -5x^2 & & 4 \\ \hline & x^3 & 9x^2 & -5x & -7 \end{array} $$

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