We can multiply polynomials by using a GRID METHOD

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

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

Fill in each empty box by multiplying the intersecting terms.

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

Combine like terms:

$$ x^4 + 6x^3-x^3-25x^2-6x^2-6x + 25x + 6 = \\ x^4+5x^3-31x^2+19x+6 $$

Polynomial Operations Calculator