Question
Subtract polynomials: $ \, \color{blue}{ 6+8x^2-3x } \, $ , $ \, \color{orangered}{ 1+7x^3+3x^2 }$.
Answer
$$ \left( \color{blue}{6+8x^2-3x} \right) - \left( \color{orangered}{1+7x^3+3x^2} \right) = -7x^3+5x^2-3x+5 $$
Explanation
Step 1: First we have to write polynomials in descending order.
$$ \begin{aligned} P(x) &= 8x^2-3x+6 \\ Q(x) &= 7x^3+3x^2+1 \\ \end{aligned} $$Step 2: Write second polynomial below the first one. Making sure like terms are lined up.
$$ \begin{array}{lrrrr} & & 8x^2 & -3x & 6 \\ \color{red}{ - } & 7x^3 & 3x^2 & & 1 \\ \hline \end{array} $$Step 3: Change ALL the signs in the second row.
$$ \begin{array}{lrrrr} & & 8x^2 & -3x & 6 \\ \color{red}{ - } & -7x^3 & -3x^2 & & -1 \\ \hline \end{array} $$Step 4: Combine like terms (add each column):
$$ \begin{array}{lrrrr} & & 8x^2 & -3x & 6 \\ \color{red}{ - } & -7x^3 & -3x^2 & & -1 \\ \hline & 7x^3 & 11x^2 & -3x & 7 \end{array} $$This page was created using
Polynomial Operations Calculator