Question
Multiply polynomial $ \, \color{blue}{ 2x^2+3x-6 } \, $ by $ \, \color{orangered}{ x-1 }$.
Answer
$$ \left( \color{blue}{2x^2+3x-6} \right) \cdot \left( \color{orangered}{x-1} \right) = 2x^3+x^2-9x+6 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2x^2} & \color{blue}{3x} & \color{blue}{-6} \\ \hline \color{blue}{x} & & & \\ \hline \color{blue}{-1} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2x^2} & \color{blue}{3x} & \color{blue}{-6} \\ \hline \color{blue}{x} & \color{orangered}{2x^3} & \color{orangered}{3x^2} & \color{orangered}{-6x} \\ \hline \color{blue}{-1} & \color{orangered}{-2x^2} & \color{orangered}{-3x} & \color{orangered}{6} \\ \hline \end{darray} $$Combine like terms:
$$ 2x^3 + 3x^2-2x^2-6x-3x + 6 = \\ 2x^3+x^2-9x+6 $$This page was created using
Polynomial Operations Calculator