Question
Subtract polynomials: $ \, \color{blue}{ 2x+x-4 } \, $ , $ \, \color{orangered}{ 3x^2-8x-2 }$.
Answer
$$ \left( \color{blue}{2x+x-4} \right) - \left( \color{orangered}{3x^2-8x-2} \right) = -3x^2+11x-2 $$
Explanation
Step 1: First we have to write polynomials in descending order.
$$ \begin{aligned} P(x) &= 3x-4 \\ Q(x) &= 3x^2-8x-2 \\ \end{aligned} $$Step 2: Write second polynomial below the first one. Making sure like terms are lined up.
$$ \begin{array}{lrrr} & & 3x & -4 \\ \color{red}{ - } & 3x^2 & -8x & -2 \\ \hline \end{array} $$Step 3: Change ALL the signs in the second row.
$$ \begin{array}{lrrr} & & 3x & -4 \\ \color{red}{ - } & -3x^2 & 8x & 2 \\ \hline \end{array} $$Step 4: Combine like terms (add each column):
$$ \begin{array}{lrrr} & & 3x & -4 \\ \color{red}{ - } & -3x^2 & 8x & 2 \\ \hline & 3x^2 & -5x & -6 \end{array} $$This page was created using
Polynomial Operations Calculator