Question
Subtract polynomials: $ \, \color{blue}{ 2x^3+8x^4+8x } \, $ , $ \, \color{orangered}{ x^4-4x^3+3x }$.
Answer
$$ \left( \color{blue}{2x^3+8x^4+8x} \right) - \left( \color{orangered}{x^4-4x^3+3x} \right) = 7x^4+6x^3+5x $$
Explanation
Step 1: First we have to write polynomials in descending order.
$$ \begin{aligned} P(x) &= 8x^4+2x^3+8x \\ Q(x) &= x^4-4x^3+3x \\ \end{aligned} $$Step 2: Write second polynomial below the first one. Making sure like terms are lined up.
$$ \begin{array}{lrrr} & 8x^4 & 2x^3 & 8x \\ \color{red}{ - } & x^4 & -4x^3 & 3x \\ \hline \end{array} $$Step 3: Change ALL the signs in the second row.
$$ \begin{array}{lrrr} & 8x^4 & 2x^3 & 8x \\ \color{red}{ - } & -x^4 & 4x^3 & -3x \\ \hline \end{array} $$Step 4: Combine like terms (add each column):
$$ \begin{array}{lrrr} & 8x^4 & 2x^3 & 8x \\ \color{red}{ - } & -x^4 & 4x^3 & -3x \\ \hline & 9x^4 & -2x^3 & 11x \end{array} $$This page was created using
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