Multiply polynomial $ \, \color{blue}{ x^2+3x+2 } \, $ by $ \, \color{orangered}{ x^3-x^2-1 }$.

$$ \left( \color{blue}{x^2+3x+2} \right) \cdot \left( \color{orangered}{x^3-x^2-1} \right) = x^5+2x^4-x^3-3x^2-3x-2 $$

We can multiply polynomials by using a GRID METHOD

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

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

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{3x} & \color{blue}{2} \\ \hline \color{blue}{x^3} & \color{orangered}{x^5} & \color{orangered}{3x^4} & \color{orangered}{2x^3} \\ \hline \color{blue}{-x^2} & \color{orangered}{-x^4} & \color{orangered}{-3x^3} & \color{orangered}{-2x^2} \\ \hline \color{blue}{-1} & \color{orangered}{-x^2} & \color{orangered}{-3x} & \color{orangered}{-2} \\ \hline \end{darray} $$

Combine like terms:

$$ x^5 + 3x^4-x^4 + 2x^3-3x^3-x^2-2x^2-3x-2 = \\ x^5+2x^4-x^3-3x^2-3x-2 $$

Polynomial Operations Calculator