We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|c|}\hline & \color{blue}{x^3} & \color{blue}{6x^2} & \color{blue}{25x} & \color{blue}{44} \\ \hline \color{blue}{x} & & & & \\ \hline \color{blue}{-1} & & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|c|}\hline & \color{blue}{x^3} & \color{blue}{6x^2} & \color{blue}{25x} & \color{blue}{44} \\ \hline \color{blue}{x} & \color{orangered}{x^4} & \color{orangered}{6x^3} & \color{orangered}{25x^2} & \color{orangered}{44x} \\ \hline \color{blue}{-1} & \color{orangered}{-x^3} & \color{orangered}{-6x^2} & \color{orangered}{-25x} & \color{orangered}{-44} \\ \hline \end{darray} $$

Combine like terms:

$$ x^4 + 6x^3-x^3 + 25x^2-6x^2 + 44x-25x-44 = \\ x^4+5x^3+19x^2+19x-44 $$

Polynomial Operations Calculator