Question
Add $ \, \color{blue}{ 4+3x^2+8x^3 } \, $ and $ \, \color{orangered}{ -7x^3+12x^5+6x^2 }$.
Answer
$$ \left( \color{blue}{4+3x^2+8x^3} \right) + \left( \color{orangered}{-7x^3+12x^5+6x^2} \right) = 12x^5+x^3+9x^2+4 $$
Explanation
Step 1: First we have to write polynomials in descending order.
$$ \begin{aligned} P(x) &= 8x^3+3x^2+4 \\ Q(x) &= 12x^5-7x^3+6x^2 \\ \end{aligned} $$Step 2: Write second polynomial below the first one. Making sure like terms are lined up.
$$ \begin{array}{lrrrr} & & 8x^3 & 3x^2 & 4 \\ \color{blue}{ + } & 12x^5 & -7x^3 & 6x^2 & \\ \hline \end{array} $$Step 3: Combine like terms (add each column):
$$ \begin{array}{lrrrr} & & 8x^3 & 3x^2 & 4 \\ \color{blue}{ + } & 12x^5 & -7x^3 & 6x^2 & \\ \hline & 12x^5 & x^3 & 9x^2 & 4 \end{array} $$This page was created using
Polynomial Operations Calculator