Question
Multiply polynomial $ \, \color{blue}{ -x-3 } \, $ by $ \, \color{orangered}{ 2x^2+5x+8 }$.
Answer
$$ \left( \color{blue}{-x-3} \right) \cdot \left( \color{orangered}{2x^2+5x+8} \right) = -2x^3-11x^2-23x-24 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2x^2} & \color{blue}{5x} & \color{blue}{8} \\ \hline \color{blue}{-x} & & & \\ \hline \color{blue}{-3} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2x^2} & \color{blue}{5x} & \color{blue}{8} \\ \hline \color{blue}{-x} & \color{orangered}{-2x^3} & \color{orangered}{-5x^2} & \color{orangered}{-8x} \\ \hline \color{blue}{-3} & \color{orangered}{-6x^2} & \color{orangered}{-15x} & \color{orangered}{-24} \\ \hline \end{darray} $$Combine like terms:
$$ -2x^3-5x^2-6x^2-8x-15x-24 = \\ -2x^3-11x^2-23x-24 $$This page was created using
Polynomial Operations Calculator