Multiply polynomial $ \, \color{blue}{ -3x-5 } \, $ by $ \, \color{orangered}{ 3x^2+x-1 }$.

$$ \left( \color{blue}{-3x-5} \right) \cdot \left( \color{orangered}{3x^2+x-1} \right) = -9x^3-18x^2-2x+5 $$

We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{3x^2} & \color{blue}{x} & \color{blue}{-1} \\ \hline \color{blue}{-3x} & & & \\ \hline \color{blue}{-5} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{3x^2} & \color{blue}{x} & \color{blue}{-1} \\ \hline \color{blue}{-3x} & \color{orangered}{-9x^3} & \color{orangered}{-3x^2} & \color{orangered}{3x} \\ \hline \color{blue}{-5} & \color{orangered}{-15x^2} & \color{orangered}{-5x} & \color{orangered}{5} \\ \hline \end{darray} $$

Combine like terms:

$$ -9x^3-3x^2-15x^2 + 3x-5x + 5 = \\ -9x^3-18x^2-2x+5 $$

Polynomial Operations Calculator