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

$$ \left( \color{blue}{2x^2-3x+5} \right) \cdot \left( \color{orangered}{x-5} \right) = 2x^3-13x^2+20x-25 $$

We can multiply polynomials by using a GRID METHOD

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

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

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2x^2} & \color{blue}{-3x} & \color{blue}{5} \\ \hline \color{blue}{x} & \color{orangered}{2x^3} & \color{orangered}{-3x^2} & \color{orangered}{5x} \\ \hline \color{blue}{-5} & \color{orangered}{-10x^2} & \color{orangered}{15x} & \color{orangered}{-25} \\ \hline \end{darray} $$

Combine like terms:

$$ 2x^3-3x^2-10x^2 + 5x + 15x-25 = \\ 2x^3-13x^2+20x-25 $$

Polynomial Operations Calculator