Question
Add $ \, \color{blue}{ 10x^2-5x^3+4-12x } \, $ and $ \, \color{orangered}{ 8x^3-4x^2+5 }$.
Answer
$$ \left( \color{blue}{10x^2-5x^3+4-12x} \right) + \left( \color{orangered}{8x^3-4x^2+5} \right) = 3x^3+6x^2-12x+9 $$
Explanation
Step 1: First we have to write polynomials in descending order.
$$ \begin{aligned} P(x) &= -5x^3+10x^2-12x+4 \\ Q(x) &= 8x^3-4x^2+5 \\ \end{aligned} $$Step 2: Write second polynomial below the first one. Making sure like terms are lined up.
$$ \begin{array}{lrrrr} & -5x^3 & 10x^2 & -12x & 4 \\ \color{blue}{ + } & 8x^3 & -4x^2 & & 5 \\ \hline \end{array} $$Step 3: Combine like terms (add each column):
$$ \begin{array}{lrrrr} & -5x^3 & 10x^2 & -12x & 4 \\ \color{blue}{ + } & 8x^3 & -4x^2 & & 5 \\ \hline & 3x^3 & 6x^2 & -12x & 9 \end{array} $$This page was created using
Polynomial Operations Calculator