Multiply polynomial $ \, \color{blue}{ x^2-x+1 } \, $ by $ \, \color{orangered}{ x^3-2x-2 }$.

$$ \left( \color{blue}{x^2-x+1} \right) \cdot \left( \color{orangered}{x^3-2x-2} \right) = x^5-x^4-x^3-2 $$

We can multiply polynomials by using a GRID METHOD

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

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

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{-x} & \color{blue}{1} \\ \hline \color{blue}{x^3} & \color{orangered}{x^5} & \color{orangered}{-x^4} & \color{orangered}{x^3} \\ \hline \color{blue}{-2x} & \color{orangered}{-2x^3} & \color{orangered}{2x^2} & \color{orangered}{-2x} \\ \hline \color{blue}{-2} & \color{orangered}{-2x^2} & \color{orangered}{2x} & \color{orangered}{-2} \\ \hline \end{darray} $$

Combine like terms:

$$ x^5-x^4-2x^3 + x^3 + 2x^2-2x^2-2x + 2x-2 = \\ x^5-x^4-x^3-2 $$

Polynomial Operations Calculator