Question
Subtract polynomials: $ \, \color{blue}{ 10-5x-4x^2 } \, $ , $ \, \color{orangered}{ x-7 }$.
Answer
$$ \left( \color{blue}{10-5x-4x^2} \right) - \left( \color{orangered}{x-7} \right) = -4x^2-6x+17 $$
Explanation
Step 1: First we have to write polynomials in descending order.
$$ \begin{aligned} P(x) &= -4x^2-5x+10 \\ Q(x) &= x-7 \\ \end{aligned} $$Step 2: Write second polynomial below the first one. Making sure like terms are lined up.
$$ \begin{array}{lrrr} & -4x^2 & -5x & 10 \\ \color{red}{ - } & & x & -7 \\ \hline \end{array} $$Step 3: Change ALL the signs in the second row.
$$ \begin{array}{lrrr} & -4x^2 & -5x & 10 \\ \color{red}{ - } & & -x & 7 \\ \hline \end{array} $$Step 4: Combine like terms (add each column):
$$ \begin{array}{lrrr} & -4x^2 & -5x & 10 \\ \color{red}{ - } & & -x & 7 \\ \hline & -4x^2 & -4x & 3 \end{array} $$This page was created using
Polynomial Operations Calculator