Question
Subtract polynomials: $ \, \color{blue}{ 5x^2+3x-2 } \, $ , $ \, \color{orangered}{ 12x^2+8-1 }$.
Answer
$$ \left( \color{blue}{5x^2+3x-2} \right) - \left( \color{orangered}{12x^2+8-1} \right) = -7x^2+3x-9 $$
Explanation
Step 1: First we have to write polynomials in descending order.
$$ \begin{aligned} P(x) &= 5x^2+3x-2 \\ Q(x) &= 12x^2+7 \\ \end{aligned} $$Step 2: Write second polynomial below the first one. Making sure like terms are lined up.
$$ \begin{array}{lrrr} & 5x^2 & 3x & -2 \\ \color{red}{ - } & 12x^2 & & 7 \\ \hline \end{array} $$Step 3: Change ALL the signs in the second row.
$$ \begin{array}{lrrr} & 5x^2 & 3x & -2 \\ \color{red}{ - } & -12x^2 & & -7 \\ \hline \end{array} $$Step 4: Combine like terms (add each column):
$$ \begin{array}{lrrr} & 5x^2 & 3x & -2 \\ \color{red}{ - } & -12x^2 & & -7 \\ \hline & 17x^2 & 3x & 5 \end{array} $$This page was created using
Polynomial Operations Calculator