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

$$ \left( \color{blue}{3x+4} \right) \cdot \left( \color{orangered}{x^2-3x-3} \right) = 3x^3-5x^2-21x-12 $$

We can multiply polynomials by using a GRID METHOD

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

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

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{-3x} & \color{blue}{-3} \\ \hline \color{blue}{3x} & \color{orangered}{3x^3} & \color{orangered}{-9x^2} & \color{orangered}{-9x} \\ \hline \color{blue}{4} & \color{orangered}{4x^2} & \color{orangered}{-12x} & \color{orangered}{-12} \\ \hline \end{darray} $$

Combine like terms:

$$ 3x^3-9x^2 + 4x^2-9x-12x-12 = \\ 3x^3-5x^2-21x-12 $$

Polynomial Operations Calculator