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

$$ \left( \color{blue}{8x-3} \right) \cdot \left( \color{orangered}{-x^2+x+3} \right) = -8x^3+11x^2+21x-9 $$

We can multiply polynomials by using a GRID METHOD

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

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

Fill in each empty box by multiplying the intersecting terms.

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

Combine like terms:

$$ -8x^3 + 8x^2 + 3x^2 + 24x-3x-9 = \\ -8x^3+11x^2+21x-9 $$

Polynomial Operations Calculator