Question
Subtract polynomials: $ \, \color{blue}{ 7-13x^3-11x } \, $ , $ \, \color{orangered}{ 2x^3+8-4x^5 }$.
Answer
$$ \left( \color{blue}{7-13x^3-11x} \right) - \left( \color{orangered}{2x^3+8-4x^5} \right) = 4x^5-15x^3-11x-1 $$
Explanation
Step 1: First we have to write polynomials in descending order.
$$ \begin{aligned} P(x) &= -13x^3-11x+7 \\ Q(x) &= -4x^5+2x^3+8 \\ \end{aligned} $$Step 2: Write second polynomial below the first one. Making sure like terms are lined up.
$$ \begin{array}{lrrrr} & & -13x^3 & -11x & 7 \\ \color{red}{ - } & -4x^5 & 2x^3 & & 8 \\ \hline \end{array} $$Step 3: Change ALL the signs in the second row.
$$ \begin{array}{lrrrr} & & -13x^3 & -11x & 7 \\ \color{red}{ - } & 4x^5 & -2x^3 & & -8 \\ \hline \end{array} $$Step 4: Combine like terms (add each column):
$$ \begin{array}{lrrrr} & & -13x^3 & -11x & 7 \\ \color{red}{ - } & 4x^5 & -2x^3 & & -8 \\ \hline & -4x^5 & -11x^3 & -11x & 15 \end{array} $$This page was created using
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