Multiply polynomial $ \, \color{blue}{ x^2+3x-28 } \, $ by $ \, \color{orangered}{ x-4 }$.

$$ \left( \color{blue}{x^2+3x-28} \right) \cdot \left( \color{orangered}{x-4} \right) = x^3-x^2-40x+112 $$

We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{3x} & \color{blue}{-28} \\ \hline \color{blue}{x} & & & \\ \hline \color{blue}{-4} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{3x} & \color{blue}{-28} \\ \hline \color{blue}{x} & \color{orangered}{x^3} & \color{orangered}{3x^2} & \color{orangered}{-28x} \\ \hline \color{blue}{-4} & \color{orangered}{-4x^2} & \color{orangered}{-12x} & \color{orangered}{112} \\ \hline \end{darray} $$

Combine like terms:

$$ x^3 + 3x^2-4x^2-28x-12x + 112 = \\ x^3-x^2-40x+112 $$

Polynomial Operations Calculator