Multiply polynomial $ \, \color{blue}{ 2x^2+6x-13 } \, $ by $ \, \color{orangered}{ x-9 }$.

$$ \left( \color{blue}{2x^2+6x-13} \right) \cdot \left( \color{orangered}{x-9} \right) = 2x^3-12x^2-67x+117 $$

We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2x^2} & \color{blue}{6x} & \color{blue}{-13} \\ \hline \color{blue}{x} & & & \\ \hline \color{blue}{-9} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2x^2} & \color{blue}{6x} & \color{blue}{-13} \\ \hline \color{blue}{x} & \color{orangered}{2x^3} & \color{orangered}{6x^2} & \color{orangered}{-13x} \\ \hline \color{blue}{-9} & \color{orangered}{-18x^2} & \color{orangered}{-54x} & \color{orangered}{117} \\ \hline \end{darray} $$

Combine like terms:

$$ 2x^3 + 6x^2-18x^2-13x-54x + 117 = \\ 2x^3-12x^2-67x+117 $$

Polynomial Operations Calculator