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