Multiply polynomial $ \, \color{blue}{ 2x+3 } \, $ by $ \, \color{orangered}{ x^2-6x+1 }$.

$$ \left( \color{blue}{2x+3} \right) \cdot \left( \color{orangered}{x^2-6x+1} \right) = 2x^3-9x^2-16x+3 $$

We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{-6x} & \color{blue}{1} \\ \hline \color{blue}{2x} & & & \\ \hline \color{blue}{3} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{-6x} & \color{blue}{1} \\ \hline \color{blue}{2x} & \color{orangered}{2x^3} & \color{orangered}{-12x^2} & \color{orangered}{2x} \\ \hline \color{blue}{3} & \color{orangered}{3x^2} & \color{orangered}{-18x} & \color{orangered}{3} \\ \hline \end{darray} $$

Combine like terms:

$$ 2x^3-12x^2 + 3x^2 + 2x-18x + 3 = \\ 2x^3-9x^2-16x+3 $$

Polynomial Operations Calculator