Question
Multiply polynomial $ \, \color{blue}{ x-2 } \, $ by $ \, \color{orangered}{ x^2+2x+4 }$.
Answer
$$ \left( \color{blue}{x-2} \right) \cdot \left( \color{orangered}{x^2+2x+4} \right) = x^3-8 $$
Explanation
We can multiply polynomials by using a GRID METHOD
Write one of the polynomials across the top and the other down the left side.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{2x} & \color{blue}{4} \\ \hline \color{blue}{x} & & & \\ \hline \color{blue}{-2} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{2x} & \color{blue}{4} \\ \hline \color{blue}{x} & \color{orangered}{x^3} & \color{orangered}{2x^2} & \color{orangered}{4x} \\ \hline \color{blue}{-2} & \color{orangered}{-2x^2} & \color{orangered}{-4x} & \color{orangered}{-8} \\ \hline \end{darray} $$Combine like terms:
$$ x^3 + 2x^2-2x^2 + 4x-4x-8 = \\ x^3-8 $$This page was created using
Polynomial Operations Calculator