Multiply polynomial $ \, \color{blue}{ 3x+8 } \, $ by $ \, \color{orangered}{ 2x^2-3x+3 }$.

$$ \left( \color{blue}{3x+8} \right) \cdot \left( \color{orangered}{2x^2-3x+3} \right) = 6x^3+7x^2-15x+24 $$

We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2x^2} & \color{blue}{-3x} & \color{blue}{3} \\ \hline \color{blue}{3x} & & & \\ \hline \color{blue}{8} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2x^2} & \color{blue}{-3x} & \color{blue}{3} \\ \hline \color{blue}{3x} & \color{orangered}{6x^3} & \color{orangered}{-9x^2} & \color{orangered}{9x} \\ \hline \color{blue}{8} & \color{orangered}{16x^2} & \color{orangered}{-24x} & \color{orangered}{24} \\ \hline \end{darray} $$

Combine like terms:

$$ 6x^3-9x^2 + 16x^2 + 9x-24x + 24 = \\ 6x^3+7x^2-15x+24 $$

Polynomial Operations Calculator