Multiply polynomial $ \, \color{blue}{ 5x^2+x+1 } \, $ by $ \, \color{orangered}{ x-2 }$.

$$ \left( \color{blue}{5x^2+x+1} \right) \cdot \left( \color{orangered}{x-2} \right) = 5x^3-9x^2-x-2 $$

We can multiply polynomials by using a GRID METHOD

Write one of the polynomials across the top and the other down the left side.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{5x^2} & \color{blue}{x} & \color{blue}{1} \\ \hline \color{blue}{x} & & & \\ \hline \color{blue}{-2} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{5x^2} & \color{blue}{x} & \color{blue}{1} \\ \hline \color{blue}{x} & \color{orangered}{5x^3} & \color{orangered}{x^2} & \color{orangered}{x} \\ \hline \color{blue}{-2} & \color{orangered}{-10x^2} & \color{orangered}{-2x} & \color{orangered}{-2} \\ \hline \end{darray} $$

Combine like terms:

$$ 5x^3 + x^2-10x^2 + x-2x-2 = \\ 5x^3-9x^2-x-2 $$

Polynomial Operations Calculator