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