Question
Multiply polynomial $ \, \color{blue}{ x+3 } \, $ by $ \, \color{orangered}{ x^2+x-3 }$.
Answer
$$ \left( \color{blue}{x+3} \right) \cdot \left( \color{orangered}{x^2+x-3} \right) = x^3+4x^2-9 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{x} & \color{blue}{-3} \\ \hline \color{blue}{x} & & & \\ \hline \color{blue}{3} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{x} & \color{blue}{-3} \\ \hline \color{blue}{x} & \color{orangered}{x^3} & \color{orangered}{x^2} & \color{orangered}{-3x} \\ \hline \color{blue}{3} & \color{orangered}{3x^2} & \color{orangered}{3x} & \color{orangered}{-9} \\ \hline \end{darray} $$Combine like terms:
$$ x^3 + x^2 + 3x^2-3x + 3x-9 = \\ x^3+4x^2-9 $$This page was created using
Polynomial Operations Calculator