Question
Subtract polynomials: $ \, \color{blue}{ 6x-4x^2-7x^3 } \, $ , $ \, \color{orangered}{ 9x^2-5x }$.
Answer
$$ \left( \color{blue}{6x-4x^2-7x^3} \right) - \left( \color{orangered}{9x^2-5x} \right) = -7x^3-13x^2+11x $$
Explanation
Step 1: First we have to write polynomials in descending order.
$$ \begin{aligned} P(x) &= -7x^3-4x^2+6x \\ Q(x) &= 9x^2-5x \\ \end{aligned} $$Step 2: Write second polynomial below the first one. Making sure like terms are lined up.
$$ \begin{array}{lrrr} & -7x^3 & -4x^2 & 6x \\ \color{red}{ - } & & 9x^2 & -5x \\ \hline \end{array} $$Step 3: Change ALL the signs in the second row.
$$ \begin{array}{lrrr} & -7x^3 & -4x^2 & 6x \\ \color{red}{ - } & & -9x^2 & 5x \\ \hline \end{array} $$Step 4: Combine like terms (add each column):
$$ \begin{array}{lrrr} & -7x^3 & -4x^2 & 6x \\ \color{red}{ - } & & -9x^2 & 5x \\ \hline & -7x^3 & 5x^2 & x \end{array} $$This page was created using
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