Question
Multiply polynomial $ \, \color{blue}{ 5x+1 } \, $ by $ \, \color{orangered}{ x^2-6x-3 }$.
Answer
$$ \left( \color{blue}{5x+1} \right) \cdot \left( \color{orangered}{x^2-6x-3} \right) = 5x^3-29x^2-21x-3 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{-6x} & \color{blue}{-3} \\ \hline \color{blue}{5x} & & & \\ \hline \color{blue}{1} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{-6x} & \color{blue}{-3} \\ \hline \color{blue}{5x} & \color{orangered}{5x^3} & \color{orangered}{-30x^2} & \color{orangered}{-15x} \\ \hline \color{blue}{1} & \color{orangered}{x^2} & \color{orangered}{-6x} & \color{orangered}{-3} \\ \hline \end{darray} $$Combine like terms:
$$ 5x^3-30x^2 + x^2-15x-6x-3 = \\ 5x^3-29x^2-21x-3 $$This page was created using
Polynomial Operations Calculator