Question
Multiply polynomial $ \, \color{blue}{ 3x+2 } \, $ by $ \, \color{orangered}{ -x^2-3x+1 }$.
Answer
$$ \left( \color{blue}{3x+2} \right) \cdot \left( \color{orangered}{-x^2-3x+1} \right) = -3x^3-11x^2-3x+2 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{-x^2} & \color{blue}{-3x} & \color{blue}{1} \\ \hline \color{blue}{3x} & & & \\ \hline \color{blue}{2} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{-x^2} & \color{blue}{-3x} & \color{blue}{1} \\ \hline \color{blue}{3x} & \color{orangered}{-3x^3} & \color{orangered}{-9x^2} & \color{orangered}{3x} \\ \hline \color{blue}{2} & \color{orangered}{-2x^2} & \color{orangered}{-6x} & \color{orangered}{2} \\ \hline \end{darray} $$Combine like terms:
$$ -3x^3-9x^2-2x^2 + 3x-6x + 2 = \\ -3x^3-11x^2-3x+2 $$This page was created using
Polynomial Operations Calculator