Question
Multiply polynomial $ \, \color{blue}{ 2x^2-19x-18 } \, $ by $ \, \color{orangered}{ x-10 }$.
Answer
$$ \left( \color{blue}{2x^2-19x-18} \right) \cdot \left( \color{orangered}{x-10} \right) = 2x^3-39x^2+172x+180 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2x^2} & \color{blue}{-19x} & \color{blue}{-18} \\ \hline \color{blue}{x} & & & \\ \hline \color{blue}{-10} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2x^2} & \color{blue}{-19x} & \color{blue}{-18} \\ \hline \color{blue}{x} & \color{orangered}{2x^3} & \color{orangered}{-19x^2} & \color{orangered}{-18x} \\ \hline \color{blue}{-10} & \color{orangered}{-20x^2} & \color{orangered}{190x} & \color{orangered}{180} \\ \hline \end{darray} $$Combine like terms:
$$ 2x^3-19x^2-20x^2-18x + 190x + 180 = \\ 2x^3-39x^2+172x+180 $$This page was created using
Polynomial Operations Calculator