Question
Multiply polynomial $ \, \color{blue}{ 2x^3-2x-3 } \, $ by $ \, \color{orangered}{ 5x+1 }$.
Answer
$$ \left( \color{blue}{2x^3-2x-3} \right) \cdot \left( \color{orangered}{5x+1} \right) = 10x^4+2x^3-10x^2-17x-3 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2x^3} & \color{blue}{-2x} & \color{blue}{-3} \\ \hline \color{blue}{5x} & & & \\ \hline \color{blue}{1} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2x^3} & \color{blue}{-2x} & \color{blue}{-3} \\ \hline \color{blue}{5x} & \color{orangered}{10x^4} & \color{orangered}{-10x^2} & \color{orangered}{-15x} \\ \hline \color{blue}{1} & \color{orangered}{2x^3} & \color{orangered}{-2x} & \color{orangered}{-3} \\ \hline \end{darray} $$Combine like terms:
$$ 10x^4-10x^2 + 2x^3-15x-2x-3 = \\ 10x^4+2x^3-10x^2-17x-3 $$This page was created using
Polynomial Operations Calculator