Question
Multiply polynomial $ \, \color{blue}{ 2x-1 } \, $ by $ \, \color{orangered}{ x^2+5x-1 }$.
Answer
$$ \left( \color{blue}{2x-1} \right) \cdot \left( \color{orangered}{x^2+5x-1} \right) = 2x^3+9x^2-7x+1 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{5x} & \color{blue}{-1} \\ \hline \color{blue}{2x} & & & \\ \hline \color{blue}{-1} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{5x} & \color{blue}{-1} \\ \hline \color{blue}{2x} & \color{orangered}{2x^3} & \color{orangered}{10x^2} & \color{orangered}{-2x} \\ \hline \color{blue}{-1} & \color{orangered}{-x^2} & \color{orangered}{-5x} & \color{orangered}{1} \\ \hline \end{darray} $$Combine like terms:
$$ 2x^3 + 10x^2-x^2-2x-5x + 1 = \\ 2x^3+9x^2-7x+1 $$This page was created using
Polynomial Operations Calculator