Multiply polynomial $ \, \color{blue}{ 3x-5 } \, $ by $ \, \color{orangered}{ x^2+2x-4 }$.

$$ \left( \color{blue}{3x-5} \right) \cdot \left( \color{orangered}{x^2+2x-4} \right) = 3x^3+x^2-22x+20 $$

We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{2x} & \color{blue}{-4} \\ \hline \color{blue}{3x} & & & \\ \hline \color{blue}{-5} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{2x} & \color{blue}{-4} \\ \hline \color{blue}{3x} & \color{orangered}{3x^3} & \color{orangered}{6x^2} & \color{orangered}{-12x} \\ \hline \color{blue}{-5} & \color{orangered}{-5x^2} & \color{orangered}{-10x} & \color{orangered}{20} \\ \hline \end{darray} $$

Combine like terms:

$$ 3x^3 + 6x^2-5x^2-12x-10x + 20 = \\ 3x^3+x^2-22x+20 $$

Polynomial Operations Calculator