Multiply polynomial $ \, \color{blue}{ x^2-3x+2 } \, $ by $ \, \color{orangered}{ x-4 }$.

$$ \left( \color{blue}{x^2-3x+2} \right) \cdot \left( \color{orangered}{x-4} \right) = x^3-7x^2+14x-8 $$

We can multiply polynomials by using a GRID METHOD

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

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

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{-3x} & \color{blue}{2} \\ \hline \color{blue}{x} & \color{orangered}{x^3} & \color{orangered}{-3x^2} & \color{orangered}{2x} \\ \hline \color{blue}{-4} & \color{orangered}{-4x^2} & \color{orangered}{12x} & \color{orangered}{-8} \\ \hline \end{darray} $$

Combine like terms:

$$ x^3-3x^2-4x^2 + 2x + 12x-8 = \\ x^3-7x^2+14x-8 $$

Polynomial Operations Calculator