Question
Multiply polynomial $ \, \color{blue}{ 3x^2+x-4 } \, $ by $ \, \color{orangered}{ x-2 }$.
Answer
$$ \left( \color{blue}{3x^2+x-4} \right) \cdot \left( \color{orangered}{x-2} \right) = 3x^3-5x^2-6x+8 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{3x^2} & \color{blue}{x} & \color{blue}{-4} \\ \hline \color{blue}{x} & & & \\ \hline \color{blue}{-2} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{3x^2} & \color{blue}{x} & \color{blue}{-4} \\ \hline \color{blue}{x} & \color{orangered}{3x^3} & \color{orangered}{x^2} & \color{orangered}{-4x} \\ \hline \color{blue}{-2} & \color{orangered}{-6x^2} & \color{orangered}{-2x} & \color{orangered}{8} \\ \hline \end{darray} $$Combine like terms:
$$ 3x^3 + x^2-6x^2-4x-2x + 8 = \\ 3x^3-5x^2-6x+8 $$This page was created using
Polynomial Operations Calculator