Subtract polynomials: $ \, \color{blue}{ 5x^3-6x^4-6 } \, $ , $ \, \color{orangered}{ 5x^3-4x+1 }$.

$$ \left( \color{blue}{5x^3-6x^4-6} \right) - \left( \color{orangered}{5x^3-4x+1} \right) = -6x^4+4x-7 $$

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

$$ \begin{aligned} P(x) &= -6x^4+5x^3-6 \\ Q(x) &= 5x^3-4x+1 \\ \end{aligned} $$

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

$$ \begin{array}{lrrrr} & -6x^4 & 5x^3 & & -6 \\ \color{red}{ - } & & 5x^3 & -4x & 1 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrrr} & -6x^4 & 5x^3 & & -6 \\ \color{red}{ - } & & -5x^3 & 4x & -1 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrrr} & -6x^4 & 5x^3 & & -6 \\ \color{red}{ - } & & -5x^3 & 4x & -1 \\ \hline & -6x^4 & 10x^3 & -4x & -5 \end{array} $$

Polynomial Operations Calculator