Multiply polynomial $ \, \color{blue}{ 3x+2 } \, $ by $ \, \color{orangered}{ -x^2-4x-6 }$.

$$ \left( \color{blue}{3x+2} \right) \cdot \left( \color{orangered}{-x^2-4x-6} \right) = -3x^3-14x^2-26x-12 $$

We can multiply polynomials by using a GRID METHOD

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

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

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{-x^2} & \color{blue}{-4x} & \color{blue}{-6} \\ \hline \color{blue}{3x} & \color{orangered}{-3x^3} & \color{orangered}{-12x^2} & \color{orangered}{-18x} \\ \hline \color{blue}{2} & \color{orangered}{-2x^2} & \color{orangered}{-8x} & \color{orangered}{-12} \\ \hline \end{darray} $$

Combine like terms:

$$ -3x^3-12x^2-2x^2-18x-8x-12 = \\ -3x^3-14x^2-26x-12 $$

Polynomial Operations Calculator