Multiply polynomial $ \, \color{blue}{ x-6 } \, $ by $ \, \color{orangered}{ x^2-2x+4 }$.

$$ \left( \color{blue}{x-6} \right) \cdot \left( \color{orangered}{x^2-2x+4} \right) = x^3-8x^2+16x-24 $$

We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{-2x} & \color{blue}{4} \\ \hline \color{blue}{x} & & & \\ \hline \color{blue}{-6} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{-2x} & \color{blue}{4} \\ \hline \color{blue}{x} & \color{orangered}{x^3} & \color{orangered}{-2x^2} & \color{orangered}{4x} \\ \hline \color{blue}{-6} & \color{orangered}{-6x^2} & \color{orangered}{12x} & \color{orangered}{-24} \\ \hline \end{darray} $$

Combine like terms:

$$ x^3-2x^2-6x^2 + 4x + 12x-24 = \\ x^3-8x^2+16x-24 $$

Polynomial Operations Calculator