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