Multiply polynomial $ \, \color{blue}{ x^2-x-2 } \, $ by $ \, \color{orangered}{ x^2+x-6 }$.

$$ \left( \color{blue}{x^2-x-2} \right) \cdot \left( \color{orangered}{x^2+x-6} \right) = x^4-9x^2+4x+12 $$

We can multiply polynomials by using a GRID METHOD

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

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

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{-x} & \color{blue}{-2} \\ \hline \color{blue}{x^2} & \color{orangered}{x^4} & \color{orangered}{-x^3} & \color{orangered}{-2x^2} \\ \hline \color{blue}{x} & \color{orangered}{x^3} & \color{orangered}{-x^2} & \color{orangered}{-2x} \\ \hline \color{blue}{-6} & \color{orangered}{-6x^2} & \color{orangered}{6x} & \color{orangered}{12} \\ \hline \end{darray} $$

Combine like terms:

$$ x^4-x^3 + x^3-2x^2-x^2-6x^2-2x + 6x + 12 = \\ x^4-9x^2+4x+12 $$

Polynomial Operations Calculator