Multiply polynomial $ \, \color{blue}{ 2x^2+5x-9 } \, $ by $ \, \color{orangered}{ 3x-17 }$.

$$ \left( \color{blue}{2x^2+5x-9} \right) \cdot \left( \color{orangered}{3x-17} \right) = 6x^3-19x^2-112x+153 $$

We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2x^2} & \color{blue}{5x} & \color{blue}{-9} \\ \hline \color{blue}{3x} & & & \\ \hline \color{blue}{-17} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2x^2} & \color{blue}{5x} & \color{blue}{-9} \\ \hline \color{blue}{3x} & \color{orangered}{6x^3} & \color{orangered}{15x^2} & \color{orangered}{-27x} \\ \hline \color{blue}{-17} & \color{orangered}{-34x^2} & \color{orangered}{-85x} & \color{orangered}{153} \\ \hline \end{darray} $$

Combine like terms:

$$ 6x^3 + 15x^2-34x^2-27x-85x + 153 = \\ 6x^3-19x^2-112x+153 $$

Polynomial Operations Calculator