Multiply polynomial $ \, \color{blue}{ -x+2 } \, $ by $ \, \color{orangered}{ x^2+9x-2 }$.

$$ \left( \color{blue}{-x+2} \right) \cdot \left( \color{orangered}{x^2+9x-2} \right) = -x^3-7x^2+20x-4 $$

We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{9x} & \color{blue}{-2} \\ \hline \color{blue}{-x} & & & \\ \hline \color{blue}{2} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{9x} & \color{blue}{-2} \\ \hline \color{blue}{-x} & \color{orangered}{-x^3} & \color{orangered}{-9x^2} & \color{orangered}{2x} \\ \hline \color{blue}{2} & \color{orangered}{2x^2} & \color{orangered}{18x} & \color{orangered}{-4} \\ \hline \end{darray} $$

Combine like terms:

$$ -x^3-9x^2 + 2x^2 + 2x + 18x-4 = \\ -x^3-7x^2+20x-4 $$

Polynomial Operations Calculator