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

$$ \left( \color{blue}{8x-2} \right) \cdot \left( \color{orangered}{-x^2+x+3} \right) = -8x^3+10x^2+22x-6 $$

We can multiply polynomials by using a GRID METHOD

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

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

Fill in each empty box by multiplying the intersecting terms.

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

Combine like terms:

$$ -8x^3 + 8x^2 + 2x^2 + 24x-2x-6 = \\ -8x^3+10x^2+22x-6 $$

Polynomial Operations Calculator