Multiply polynomial $ \, \color{blue}{ x+1 } \, $ by $ \, \color{orangered}{ x^2+2x-5 }$.

$$ \left( \color{blue}{x+1} \right) \cdot \left( \color{orangered}{x^2+2x-5} \right) = x^3+3x^2-3x-5 $$

We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{2x} & \color{blue}{-5} \\ \hline \color{blue}{x} & & & \\ \hline \color{blue}{1} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{2x} & \color{blue}{-5} \\ \hline \color{blue}{x} & \color{orangered}{x^3} & \color{orangered}{2x^2} & \color{orangered}{-5x} \\ \hline \color{blue}{1} & \color{orangered}{x^2} & \color{orangered}{2x} & \color{orangered}{-5} \\ \hline \end{darray} $$

Combine like terms:

$$ x^3 + 2x^2 + x^2-5x + 2x-5 = \\ x^3+3x^2-3x-5 $$

Polynomial Operations Calculator