Question
Multiply polynomial $ \, \color{blue}{ 5x-2 } \, $ by $ \, \color{orangered}{ x^2-5x+2 }$.
Answer
$$ \left( \color{blue}{5x-2} \right) \cdot \left( \color{orangered}{x^2-5x+2} \right) = 5x^3-27x^2+20x-4 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{-5x} & \color{blue}{2} \\ \hline \color{blue}{5x} & & & \\ \hline \color{blue}{-2} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{-5x} & \color{blue}{2} \\ \hline \color{blue}{5x} & \color{orangered}{5x^3} & \color{orangered}{-25x^2} & \color{orangered}{10x} \\ \hline \color{blue}{-2} & \color{orangered}{-2x^2} & \color{orangered}{10x} & \color{orangered}{-4} \\ \hline \end{darray} $$Combine like terms:
$$ 5x^3-25x^2-2x^2 + 10x + 10x-4 = \\ 5x^3-27x^2+20x-4 $$This page was created using
Polynomial Operations Calculator