Question
Multiply polynomial $ \, \color{blue}{ x^3-4x-2 } \, $ by $ \, \color{orangered}{ x^2-6 }$.
Answer
$$ \left( \color{blue}{x^3-4x-2} \right) \cdot \left( \color{orangered}{x^2-6} \right) = x^5-10x^3-2x^2+24x+12 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^3} & \color{blue}{-4x} & \color{blue}{-2} \\ \hline \color{blue}{x^2} & & & \\ \hline \color{blue}{-6} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^3} & \color{blue}{-4x} & \color{blue}{-2} \\ \hline \color{blue}{x^2} & \color{orangered}{x^5} & \color{orangered}{-4x^3} & \color{orangered}{-2x^2} \\ \hline \color{blue}{-6} & \color{orangered}{-6x^3} & \color{orangered}{24x} & \color{orangered}{12} \\ \hline \end{darray} $$Combine like terms:
$$ x^5-4x^3-6x^3-2x^2 + 24x + 12 = \\ x^5-10x^3-2x^2+24x+12 $$This page was created using
Polynomial Operations Calculator