Question
Multiply polynomial $ \, \color{blue}{ 2x^3+4x^2-5 } \, $ by $ \, \color{orangered}{ 3x-1 }$.
Answer
$$ \left( \color{blue}{2x^3+4x^2-5} \right) \cdot \left( \color{orangered}{3x-1} \right) = 6x^4+10x^3-4x^2-15x+5 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2x^3} & \color{blue}{4x^2} & \color{blue}{-5} \\ \hline \color{blue}{3x} & & & \\ \hline \color{blue}{-1} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2x^3} & \color{blue}{4x^2} & \color{blue}{-5} \\ \hline \color{blue}{3x} & \color{orangered}{6x^4} & \color{orangered}{12x^3} & \color{orangered}{-15x} \\ \hline \color{blue}{-1} & \color{orangered}{-2x^3} & \color{orangered}{-4x^2} & \color{orangered}{5} \\ \hline \end{darray} $$Combine like terms:
$$ 6x^4 + 12x^3-2x^3-15x-4x^2 + 5 = \\ 6x^4+10x^3-4x^2-15x+5 $$This page was created using
Polynomial Operations Calculator