Question
Multiply polynomial $ \, \color{blue}{ 2x^3-5x^2+3x } \, $ by $ \, \color{orangered}{ 2x+5 }$.
Answer
$$ \left( \color{blue}{2x^3-5x^2+3x} \right) \cdot \left( \color{orangered}{2x+5} \right) = 4x^4-19x^2+15x $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2x^3} & \color{blue}{-5x^2} & \color{blue}{3x} \\ \hline \color{blue}{2x} & & & \\ \hline \color{blue}{5} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2x^3} & \color{blue}{-5x^2} & \color{blue}{3x} \\ \hline \color{blue}{2x} & \color{orangered}{4x^4} & \color{orangered}{-10x^3} & \color{orangered}{6x^2} \\ \hline \color{blue}{5} & \color{orangered}{10x^3} & \color{orangered}{-25x^2} & \color{orangered}{15x} \\ \hline \end{darray} $$Combine like terms:
$$ 4x^4-10x^3 + 10x^3 + 6x^2-25x^2 + 15x = \\ 4x^4-19x^2+15x $$This page was created using
Polynomial Operations Calculator