Question
Multiply polynomial $ \, \color{blue}{ 6x^2+3x+1 } \, $ by $ \, \color{orangered}{ 2x+5 }$.
Answer
$$ \left( \color{blue}{6x^2+3x+1} \right) \cdot \left( \color{orangered}{2x+5} \right) = 12x^3+36x^2+17x+5 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{6x^2} & \color{blue}{3x} & \color{blue}{1} \\ \hline \color{blue}{2x} & & & \\ \hline \color{blue}{5} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{6x^2} & \color{blue}{3x} & \color{blue}{1} \\ \hline \color{blue}{2x} & \color{orangered}{12x^3} & \color{orangered}{6x^2} & \color{orangered}{2x} \\ \hline \color{blue}{5} & \color{orangered}{30x^2} & \color{orangered}{15x} & \color{orangered}{5} \\ \hline \end{darray} $$Combine like terms:
$$ 12x^3 + 6x^2 + 30x^2 + 2x + 15x + 5 = \\ 12x^3+36x^2+17x+5 $$This page was created using
Polynomial Operations Calculator