Question
Subtract polynomials: $ \, \color{blue}{ 5x^2-2x^3+x } \, $ , $ \, \color{orangered}{ 6x^3-8x^2-x }$.
Answer
$$ \left( \color{blue}{5x^2-2x^3+x} \right) - \left( \color{orangered}{6x^3-8x^2-x} \right) = -8x^3+13x^2+2x $$
Explanation
Step 1: First we have to write polynomials in descending order.
$$ \begin{aligned} P(x) &= -2x^3+5x^2+x \\ Q(x) &= 6x^3-8x^2-x \\ \end{aligned} $$Step 2: Write second polynomial below the first one. Making sure like terms are lined up.
$$ \begin{array}{lrrr} & -2x^3 & 5x^2 & x \\ \color{red}{ - } & 6x^3 & -8x^2 & -x \\ \hline \end{array} $$Step 3: Change ALL the signs in the second row.
$$ \begin{array}{lrrr} & -2x^3 & 5x^2 & x \\ \color{red}{ - } & -6x^3 & 8x^2 & x \\ \hline \end{array} $$Step 4: Combine like terms (add each column):
$$ \begin{array}{lrrr} & -2x^3 & 5x^2 & x \\ \color{red}{ - } & -6x^3 & 8x^2 & x \\ \hline & 4x^3 & -3x^2 & \end{array} $$This page was created using
Polynomial Operations Calculator