Question
Multiply polynomial $ \, \color{blue}{ 2x+5 } \, $ by $ \, \color{orangered}{ 3x^3-x^2+x }$.
Answer
$$ \left( \color{blue}{2x+5} \right) \cdot \left( \color{orangered}{3x^3-x^2+x} \right) = 6x^4+13x^3-3x^2+5x $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{3x^3} & \color{blue}{-x^2} & \color{blue}{x} \\ \hline \color{blue}{2x} & & & \\ \hline \color{blue}{5} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{3x^3} & \color{blue}{-x^2} & \color{blue}{x} \\ \hline \color{blue}{2x} & \color{orangered}{6x^4} & \color{orangered}{-2x^3} & \color{orangered}{2x^2} \\ \hline \color{blue}{5} & \color{orangered}{15x^3} & \color{orangered}{-5x^2} & \color{orangered}{5x} \\ \hline \end{darray} $$Combine like terms:
$$ 6x^4-2x^3 + 15x^3 + 2x^2-5x^2 + 5x = \\ 6x^4+13x^3-3x^2+5x $$This page was created using
Polynomial Operations Calculator