Multiply polynomial $ \, \color{blue}{ -4x-3 } \, $ by $ \, \color{orangered}{ 3x^2-x-1 }$.

$$ \left( \color{blue}{-4x-3} \right) \cdot \left( \color{orangered}{3x^2-x-1} \right) = -12x^3-5x^2+7x+3 $$

We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{3x^2} & \color{blue}{-x} & \color{blue}{-1} \\ \hline \color{blue}{-4x} & & & \\ \hline \color{blue}{-3} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{3x^2} & \color{blue}{-x} & \color{blue}{-1} \\ \hline \color{blue}{-4x} & \color{orangered}{-12x^3} & \color{orangered}{4x^2} & \color{orangered}{4x} \\ \hline \color{blue}{-3} & \color{orangered}{-9x^2} & \color{orangered}{3x} & \color{orangered}{3} \\ \hline \end{darray} $$

Combine like terms:

$$ -12x^3 + 4x^2-9x^2 + 4x + 3x + 3 = \\ -12x^3-5x^2+7x+3 $$

Polynomial Operations Calculator