Question
Multiply polynomial $ \, \color{blue}{ 2x-5 } \, $ by $ \, \color{orangered}{ 5x^2+4x+7 }$.
Answer
$$ \left( \color{blue}{2x-5} \right) \cdot \left( \color{orangered}{5x^2+4x+7} \right) = 10x^3-17x^2-6x-35 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{5x^2} & \color{blue}{4x} & \color{blue}{7} \\ \hline \color{blue}{2x} & & & \\ \hline \color{blue}{-5} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{5x^2} & \color{blue}{4x} & \color{blue}{7} \\ \hline \color{blue}{2x} & \color{orangered}{10x^3} & \color{orangered}{8x^2} & \color{orangered}{14x} \\ \hline \color{blue}{-5} & \color{orangered}{-25x^2} & \color{orangered}{-20x} & \color{orangered}{-35} \\ \hline \end{darray} $$Combine like terms:
$$ 10x^3 + 8x^2-25x^2 + 14x-20x-35 = \\ 10x^3-17x^2-6x-35 $$This page was created using
Polynomial Operations Calculator