Multiply polynomial $ \, \color{blue}{ x^3+13x^2+60x+100 } \, $ by $ \, \color{orangered}{ x+5 }$.

$$ \left( \color{blue}{x^3+13x^2+60x+100} \right) \cdot \left( \color{orangered}{x+5} \right) = x^4+18x^3+125x^2+400x+500 $$

We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|c|}\hline & \color{blue}{x^3} & \color{blue}{13x^2} & \color{blue}{60x} & \color{blue}{100} \\ \hline \color{blue}{x} & & & & \\ \hline \color{blue}{5} & & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|c|}\hline & \color{blue}{x^3} & \color{blue}{13x^2} & \color{blue}{60x} & \color{blue}{100} \\ \hline \color{blue}{x} & \color{orangered}{x^4} & \color{orangered}{13x^3} & \color{orangered}{60x^2} & \color{orangered}{100x} \\ \hline \color{blue}{5} & \color{orangered}{5x^3} & \color{orangered}{65x^2} & \color{orangered}{300x} & \color{orangered}{500} \\ \hline \end{darray} $$

Combine like terms:

$$ x^4 + 13x^3 + 5x^3 + 60x^2 + 65x^2 + 100x + 300x + 500 = \\ x^4+18x^3+125x^2+400x+500 $$

Polynomial Operations Calculator