Question
Multiply polynomial $ \, \color{blue}{ x^2-2 } \, $ by $ \, \color{orangered}{ x^5-9x+3 }$.
Answer
$$ \left( \color{blue}{x^2-2} \right) \cdot \left( \color{orangered}{x^5-9x+3} \right) = x^7-2x^5-9x^3+3x^2+18x-6 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^5} & \color{blue}{-9x} & \color{blue}{3} \\ \hline \color{blue}{x^2} & & & \\ \hline \color{blue}{-2} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^5} & \color{blue}{-9x} & \color{blue}{3} \\ \hline \color{blue}{x^2} & \color{orangered}{x^7} & \color{orangered}{-9x^3} & \color{orangered}{3x^2} \\ \hline \color{blue}{-2} & \color{orangered}{-2x^5} & \color{orangered}{18x} & \color{orangered}{-6} \\ \hline \end{darray} $$Combine like terms:
$$ x^7-9x^3-2x^5 + 3x^2 + 18x-6 = \\ x^7-2x^5-9x^3+3x^2+18x-6 $$This page was created using
Polynomial Operations Calculator