Question
Multiply polynomial $ \, \color{blue}{ -x^2-4x+1 } \, $ by $ \, \color{orangered}{ 2x^2-9 }$.
Answer
$$ \left( \color{blue}{-x^2-4x+1} \right) \cdot \left( \color{orangered}{2x^2-9} \right) = -2x^4-8x^3+11x^2+36x-9 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{-x^2} & \color{blue}{-4x} & \color{blue}{1} \\ \hline \color{blue}{2x^2} & & & \\ \hline \color{blue}{-9} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{-x^2} & \color{blue}{-4x} & \color{blue}{1} \\ \hline \color{blue}{2x^2} & \color{orangered}{-2x^4} & \color{orangered}{-8x^3} & \color{orangered}{2x^2} \\ \hline \color{blue}{-9} & \color{orangered}{9x^2} & \color{orangered}{36x} & \color{orangered}{-9} \\ \hline \end{darray} $$Combine like terms:
$$ -2x^4-8x^3 + 9x^2 + 2x^2 + 36x-9 = \\ -2x^4-8x^3+11x^2+36x-9 $$This page was created using
Polynomial Operations Calculator