Question
Multiply polynomial $ \, \color{blue}{ 2x^3-2x-3 } \, $ by $ \, \color{orangered}{ -19x^2-2 }$.
Answer
$$ \left( \color{blue}{2x^3-2x-3} \right) \cdot \left( \color{orangered}{-19x^2-2} \right) = -38x^5+34x^3+57x^2+4x+6 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2x^3} & \color{blue}{-2x} & \color{blue}{-3} \\ \hline \color{blue}{-19x^2} & & & \\ \hline \color{blue}{-2} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2x^3} & \color{blue}{-2x} & \color{blue}{-3} \\ \hline \color{blue}{-19x^2} & \color{orangered}{-38x^5} & \color{orangered}{38x^3} & \color{orangered}{57x^2} \\ \hline \color{blue}{-2} & \color{orangered}{-4x^3} & \color{orangered}{4x} & \color{orangered}{6} \\ \hline \end{darray} $$Combine like terms:
$$ -38x^5 + 38x^3-4x^3 + 57x^2 + 4x + 6 = \\ -38x^5+34x^3+57x^2+4x+6 $$This page was created using
Polynomial Operations Calculator