We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{5x} & \color{blue}{4} \\ \hline \color{blue}{x^2} & & & \\ \hline \color{blue}{-6x} & & & \\ \hline \color{blue}{9} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{5x} & \color{blue}{4} \\ \hline \color{blue}{x^2} & \color{orangered}{x^4} & \color{orangered}{5x^3} & \color{orangered}{4x^2} \\ \hline \color{blue}{-6x} & \color{orangered}{-6x^3} & \color{orangered}{-30x^2} & \color{orangered}{-24x} \\ \hline \color{blue}{9} & \color{orangered}{9x^2} & \color{orangered}{45x} & \color{orangered}{36} \\ \hline \end{darray} $$

Combine like terms:

$$ x^4 + 5x^3-6x^3 + 4x^2-30x^2 + 9x^2-24x + 45x + 36 = \\ x^4-x^3-17x^2+21x+36 $$

Polynomial Operations Calculator