Multiply polynomial $ \, \color{blue}{ x+6 } \, $ by $ \, \color{orangered}{ 2x^2+x-1 }$.

$$ \left( \color{blue}{x+6} \right) \cdot \left( \color{orangered}{2x^2+x-1} \right) = 2x^3+13x^2+5x-6 $$

We can multiply polynomials by using a GRID METHOD

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

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

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2x^2} & \color{blue}{x} & \color{blue}{-1} \\ \hline \color{blue}{x} & \color{orangered}{2x^3} & \color{orangered}{x^2} & \color{orangered}{-x} \\ \hline \color{blue}{6} & \color{orangered}{12x^2} & \color{orangered}{6x} & \color{orangered}{-6} \\ \hline \end{darray} $$

Combine like terms:

$$ 2x^3 + x^2 + 12x^2-x + 6x-6 = \\ 2x^3+13x^2+5x-6 $$

Polynomial Operations Calculator