Question
Multiply polynomial $ \, \color{blue}{ 2x-5 } \, $ by $ \, \color{orangered}{ 3x^2+4x-8 }$.
Answer
$$ \left( \color{blue}{2x-5} \right) \cdot \left( \color{orangered}{3x^2+4x-8} \right) = 6x^3-7x^2-36x+40 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{3x^2} & \color{blue}{4x} & \color{blue}{-8} \\ \hline \color{blue}{2x} & & & \\ \hline \color{blue}{-5} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{3x^2} & \color{blue}{4x} & \color{blue}{-8} \\ \hline \color{blue}{2x} & \color{orangered}{6x^3} & \color{orangered}{8x^2} & \color{orangered}{-16x} \\ \hline \color{blue}{-5} & \color{orangered}{-15x^2} & \color{orangered}{-20x} & \color{orangered}{40} \\ \hline \end{darray} $$Combine like terms:
$$ 6x^3 + 8x^2-15x^2-16x-20x + 40 = \\ 6x^3-7x^2-36x+40 $$This page was created using
Polynomial Operations Calculator