Question
Subtract polynomials: $ \, \color{blue}{ 7x^3-x^4+3x^5+4x } \, $ , $ \, \color{orangered}{ -x^4-x^2+10x^5+4x^3 }$.
Answer
$$ \left( \color{blue}{7x^3-x^4+3x^5+4x} \right) - \left( \color{orangered}{-x^4-x^2+10x^5+4x^3} \right) = -7x^5+3x^3+x^2+4x $$
Explanation
Step 1: First we have to write polynomials in descending order.
$$ \begin{aligned} P(x) &= 3x^5-x^4+7x^3+4x \\ Q(x) &= 10x^5-x^4+4x^3-x^2 \\ \end{aligned} $$Step 2: Write second polynomial below the first one. Making sure like terms are lined up.
$$ \begin{array}{lrrrrr} & 3x^5 & -x^4 & 7x^3 & & 4x \\ \color{red}{ - } & 10x^5 & -x^4 & 4x^3 & -x^2 & \\ \hline \end{array} $$Step 3: Change ALL the signs in the second row.
$$ \begin{array}{lrrrrr} & 3x^5 & -x^4 & 7x^3 & & 4x \\ \color{red}{ - } & -10x^5 & x^4 & -4x^3 & x^2 & \\ \hline \end{array} $$Step 4: Combine like terms (add each column):
$$ \begin{array}{lrrrrr} & 3x^5 & -x^4 & 7x^3 & & 4x \\ \color{red}{ - } & -10x^5 & x^4 & -4x^3 & x^2 & \\ \hline & 13x^5 & -2x^4 & 11x^3 & -x^2 & 4x \end{array} $$This page was created using
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