Subtract polynomials: $ \, \color{blue}{ 3x^4-5x+2 } \, $ , $ \, \color{orangered}{ 4x^2-6x-2 }$.

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

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

$$ \begin{array}{lrrrr} & 3x^4 & & -5x & 2 \\ \color{red}{ - } & & 4x^2 & -6x & -2 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrrr} & 3x^4 & & -5x & 2 \\ \color{red}{ - } & & -4x^2 & 6x & 2 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrrr} & 3x^4 & & -5x & 2 \\ \color{red}{ - } & & -4x^2 & 6x & 2 \\ \hline & 3x^4 & 4x^2 & -11x & \end{array} $$

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