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

$$ \left( \color{blue}{4x^3+3x^2-x+2} \right) - \left( \color{orangered}{5x^3-3x^2+x-4} \right) = -x^3+6x^2-2x+6 $$

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

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

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

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

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

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

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