Question
Subtract polynomials: $ \, \color{blue}{ 8x^4-2x^2+x-4 } \, $ , $ \, \color{orangered}{ 3x^3-12x^2+8x }$.
Answer
$$ \left( \color{blue}{8x^4-2x^2+x-4} \right) - \left( \color{orangered}{3x^3-12x^2+8x} \right) = 8x^4-3x^3+10x^2-7x-4 $$
Explanation
Step 1: Write second polynomial below the first one. Making sure like terms are lined up.
$$ \begin{array}{lrrrrr} & 8x^4 & & -2x^2 & x & -4 \\ \color{red}{ - } & & 3x^3 & -12x^2 & 8x & \\ \hline \end{array} $$Step 2: Change ALL the signs in the second row.
$$ \begin{array}{lrrrrr} & 8x^4 & & -2x^2 & x & -4 \\ \color{red}{ - } & & -3x^3 & 12x^2 & -8x & \\ \hline \end{array} $$Step 3: Combine like terms (add each column):
$$ \begin{array}{lrrrrr} & 8x^4 & & -2x^2 & x & -4 \\ \color{red}{ - } & & -3x^3 & 12x^2 & -8x & \\ \hline & 8x^4 & 3x^3 & -14x^2 & 9x & -4 \end{array} $$This page was created using
Polynomial Operations Calculator