Question
Multiply polynomial $ \, \color{blue}{ x^6+x^4+3x } \, $ by $ \, \color{orangered}{ 2x+5 }$.
Answer
$$ \left( \color{blue}{x^6+x^4+3x} \right) \cdot \left( \color{orangered}{2x+5} \right) = 2x^7+5x^6+2x^5+5x^4+6x^2+15x $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^6} & \color{blue}{x^4} & \color{blue}{3x} \\ \hline \color{blue}{2x} & & & \\ \hline \color{blue}{5} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^6} & \color{blue}{x^4} & \color{blue}{3x} \\ \hline \color{blue}{2x} & \color{orangered}{2x^7} & \color{orangered}{2x^5} & \color{orangered}{6x^2} \\ \hline \color{blue}{5} & \color{orangered}{5x^6} & \color{orangered}{5x^4} & \color{orangered}{15x} \\ \hline \end{darray} $$Combine like terms:
$$ 2x^7 + 2x^5 + 5x^6 + 6x^2 + 5x^4 + 15x = \\ 2x^7+5x^6+2x^5+5x^4+6x^2+15x $$This page was created using
Polynomial Operations Calculator