Question
Subtract polynomials: $ \, \color{blue}{ 5x^2+x^3-5+6x } \, $ , $ \, \color{orangered}{ 3-3x }$.
Answer
$$ \left( \color{blue}{5x^2+x^3-5+6x} \right) - \left( \color{orangered}{3-3x} \right) = x^3+5x^2+9x-8 $$
Explanation
Step 1: First we have to write polynomials in descending order.
$$ \begin{aligned} P(x) &= x^3+5x^2+6x-5 \\ Q(x) &= -3x+3 \\ \end{aligned} $$Step 2: Write second polynomial below the first one. Making sure like terms are lined up.
$$ \begin{array}{lrrrr} & x^3 & 5x^2 & 6x & -5 \\ \color{red}{ - } & & & -3x & 3 \\ \hline \end{array} $$Step 3: Change ALL the signs in the second row.
$$ \begin{array}{lrrrr} & x^3 & 5x^2 & 6x & -5 \\ \color{red}{ - } & & & 3x & -3 \\ \hline \end{array} $$Step 4: Combine like terms (add each column):
$$ \begin{array}{lrrrr} & x^3 & 5x^2 & 6x & -5 \\ \color{red}{ - } & & & 3x & -3 \\ \hline & x^3 & 5x^2 & 3x & -2 \end{array} $$This page was created using
Polynomial Operations Calculator