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

$$ \left( \color{blue}{3x+2} \right) \cdot \left( \color{orangered}{2x^2-5x+4} \right) = 6x^3-11x^2+2x+8 $$

We can multiply polynomials by using a GRID METHOD

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

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

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2x^2} & \color{blue}{-5x} & \color{blue}{4} \\ \hline \color{blue}{3x} & \color{orangered}{6x^3} & \color{orangered}{-15x^2} & \color{orangered}{12x} \\ \hline \color{blue}{2} & \color{orangered}{4x^2} & \color{orangered}{-10x} & \color{orangered}{8} \\ \hline \end{darray} $$

Combine like terms:

$$ 6x^3-15x^2 + 4x^2 + 12x-10x + 8 = \\ 6x^3-11x^2+2x+8 $$

Polynomial Operations Calculator