Question
Multiply polynomial $ \, \color{blue}{ x^2+5x+10 } \, $ by $ \, \color{orangered}{ x+1 }$.
Answer
$$ \left( \color{blue}{x^2+5x+10} \right) \cdot \left( \color{orangered}{x+1} \right) = x^3+6x^2+15x+10 $$
Explanation
We can multiply polynomials by using a GRID METHOD
Write one of the polynomials across the top and the other down the left side.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{5x} & \color{blue}{10} \\ \hline \color{blue}{x} & & & \\ \hline \color{blue}{1} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{5x} & \color{blue}{10} \\ \hline \color{blue}{x} & \color{orangered}{x^3} & \color{orangered}{5x^2} & \color{orangered}{10x} \\ \hline \color{blue}{1} & \color{orangered}{x^2} & \color{orangered}{5x} & \color{orangered}{10} \\ \hline \end{darray} $$Combine like terms:
$$ x^3 + 5x^2 + x^2 + 10x + 5x + 10 = \\ x^3+6x^2+15x+10 $$This page was created using
Polynomial Operations Calculator