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