Multiply polynomial $ \, \color{blue}{ x-2 } \, $ by $ \, \color{orangered}{ x^3+7x+2 }$.

$$ \left( \color{blue}{x-2} \right) \cdot \left( \color{orangered}{x^3+7x+2} \right) = x^4-2x^3+7x^2-12x-4 $$

We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^3} & \color{blue}{7x} & \color{blue}{2} \\ \hline \color{blue}{x} & & & \\ \hline \color{blue}{-2} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^3} & \color{blue}{7x} & \color{blue}{2} \\ \hline \color{blue}{x} & \color{orangered}{x^4} & \color{orangered}{7x^2} & \color{orangered}{2x} \\ \hline \color{blue}{-2} & \color{orangered}{-2x^3} & \color{orangered}{-14x} & \color{orangered}{-4} \\ \hline \end{darray} $$

Combine like terms:

$$ x^4 + 7x^2-2x^3 + 2x-14x-4 = \\ x^4-2x^3+7x^2-12x-4 $$

Polynomial Operations Calculator