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