Question
Multiply polynomial $ \, \color{blue}{ x^2+x+2 } \, $ by $ \, \color{orangered}{ x^2-10x }$.
Answer
$$ \left( \color{blue}{x^2+x+2} \right) \cdot \left( \color{orangered}{x^2-10x} \right) = x^4-9x^3-8x^2-20x $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{x} & \color{blue}{2} \\ \hline \color{blue}{x^2} & & & \\ \hline \color{blue}{-10x} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{x} & \color{blue}{2} \\ \hline \color{blue}{x^2} & \color{orangered}{x^4} & \color{orangered}{x^3} & \color{orangered}{2x^2} \\ \hline \color{blue}{-10x} & \color{orangered}{-10x^3} & \color{orangered}{-10x^2} & \color{orangered}{-20x} \\ \hline \end{darray} $$Combine like terms:
$$ x^4 + x^3-10x^3 + 2x^2-10x^2-20x = \\ x^4-9x^3-8x^2-20x $$This page was created using
Polynomial Operations Calculator