Question
Subtract polynomials: $ \, \color{blue}{ -14+3x^2+2x } \, $ , $ \, \color{orangered}{ -5x+10-7x^2 }$.
Answer
$$ \left( \color{blue}{-14+3x^2+2x} \right) - \left( \color{orangered}{-5x+10-7x^2} \right) = 10x^2+7x-24 $$
Explanation
Step 1: First we have to write polynomials in descending order.
$$ \begin{aligned} P(x) &= 3x^2+2x-14 \\ Q(x) &= -7x^2-5x+10 \\ \end{aligned} $$Step 2: Write second polynomial below the first one. Making sure like terms are lined up.
$$ \begin{array}{lrrr} & 3x^2 & 2x & -14 \\ \color{red}{ - } & -7x^2 & -5x & 10 \\ \hline \end{array} $$Step 3: Change ALL the signs in the second row.
$$ \begin{array}{lrrr} & 3x^2 & 2x & -14 \\ \color{red}{ - } & 7x^2 & 5x & -10 \\ \hline \end{array} $$Step 4: Combine like terms (add each column):
$$ \begin{array}{lrrr} & 3x^2 & 2x & -14 \\ \color{red}{ - } & 7x^2 & 5x & -10 \\ \hline & -4x^2 & -3x & -4 \end{array} $$This page was created using
Polynomial Operations Calculator