Question
Multiply polynomial $ \, \color{blue}{ x^2-x-6 } \, $ by $ \, \color{orangered}{ 3x+1 }$.
Answer
$$ \left( \color{blue}{x^2-x-6} \right) \cdot \left( \color{orangered}{3x+1} \right) = 3x^3-2x^2-19x-6 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{-x} & \color{blue}{-6} \\ \hline \color{blue}{3x} & & & \\ \hline \color{blue}{1} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{-x} & \color{blue}{-6} \\ \hline \color{blue}{3x} & \color{orangered}{3x^3} & \color{orangered}{-3x^2} & \color{orangered}{-18x} \\ \hline \color{blue}{1} & \color{orangered}{x^2} & \color{orangered}{-x} & \color{orangered}{-6} \\ \hline \end{darray} $$Combine like terms:
$$ 3x^3-3x^2 + x^2-18x-x-6 = \\ 3x^3-2x^2-19x-6 $$This page was created using
Polynomial Operations Calculator