Question
Multiply polynomial $ \, \color{blue}{ 3x^2-5x-2 } \, $ by $ \, \color{orangered}{ 2x+5 }$.
Answer
$$ \left( \color{blue}{3x^2-5x-2} \right) \cdot \left( \color{orangered}{2x+5} \right) = 6x^3+5x^2-29x-10 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{3x^2} & \color{blue}{-5x} & \color{blue}{-2} \\ \hline \color{blue}{2x} & & & \\ \hline \color{blue}{5} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{3x^2} & \color{blue}{-5x} & \color{blue}{-2} \\ \hline \color{blue}{2x} & \color{orangered}{6x^3} & \color{orangered}{-10x^2} & \color{orangered}{-4x} \\ \hline \color{blue}{5} & \color{orangered}{15x^2} & \color{orangered}{-25x} & \color{orangered}{-10} \\ \hline \end{darray} $$Combine like terms:
$$ 6x^3-10x^2 + 15x^2-4x-25x-10 = \\ 6x^3+5x^2-29x-10 $$This page was created using
Polynomial Operations Calculator