Question
Subtract polynomials: $ \, \color{blue}{ x^4-5x^2+x } \, $ , $ \, \color{orangered}{ 3x^4-2x^3+x+4 }$.
Answer
$$ \left( \color{blue}{x^4-5x^2+x} \right) - \left( \color{orangered}{3x^4-2x^3+x+4} \right) = -2x^4+2x^3-5x^2-4 $$
Explanation
Step 1: Write second polynomial below the first one. Making sure like terms are lined up.
$$ \begin{array}{lrrrrr} & x^4 & & -5x^2 & x & \\ \color{red}{ - } & 3x^4 & -2x^3 & & x & 4 \\ \hline \end{array} $$Step 2: Change ALL the signs in the second row.
$$ \begin{array}{lrrrrr} & x^4 & & -5x^2 & x & \\ \color{red}{ - } & -3x^4 & 2x^3 & & -x & -4 \\ \hline \end{array} $$Step 3: Combine like terms (add each column):
$$ \begin{array}{lrrrrr} & x^4 & & -5x^2 & x & \\ \color{red}{ - } & -3x^4 & 2x^3 & & -x & -4 \\ \hline & 4x^4 & -2x^3 & -5x^2 & 2x & 4 \end{array} $$This page was created using
Polynomial Operations Calculator