Question
Subtract polynomials: $ \, \color{blue}{ 3x+3x^2+9 } \, $ , $ \, \color{orangered}{ 5x^3-7x^2+6x-9 }$.
Answer
$$ \left( \color{blue}{3x+3x^2+9} \right) - \left( \color{orangered}{5x^3-7x^2+6x-9} \right) = -5x^3+10x^2-3x+18 $$
Explanation
Step 1: First we have to write polynomials in descending order.
$$ \begin{aligned} P(x) &= 3x^2+3x+9 \\ Q(x) &= 5x^3-7x^2+6x-9 \\ \end{aligned} $$Step 2: Write second polynomial below the first one. Making sure like terms are lined up.
$$ \begin{array}{lrrrr} & & 3x^2 & 3x & 9 \\ \color{red}{ - } & 5x^3 & -7x^2 & 6x & -9 \\ \hline \end{array} $$Step 3: Change ALL the signs in the second row.
$$ \begin{array}{lrrrr} & & 3x^2 & 3x & 9 \\ \color{red}{ - } & -5x^3 & 7x^2 & -6x & 9 \\ \hline \end{array} $$Step 4: Combine like terms (add each column):
$$ \begin{array}{lrrrr} & & 3x^2 & 3x & 9 \\ \color{red}{ - } & -5x^3 & 7x^2 & -6x & 9 \\ \hline & 5x^3 & -4x^2 & 9x & \end{array} $$This page was created using
Polynomial Operations Calculator