Question
Multiply polynomial $ \, \color{blue}{ 3x-5 } \, $ by $ \, \color{orangered}{ 4x^3+2x-1 }$.
Answer
$$ \left( \color{blue}{3x-5} \right) \cdot \left( \color{orangered}{4x^3+2x-1} \right) = 12x^4-20x^3+6x^2-13x+5 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{4x^3} & \color{blue}{2x} & \color{blue}{-1} \\ \hline \color{blue}{3x} & & & \\ \hline \color{blue}{-5} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{4x^3} & \color{blue}{2x} & \color{blue}{-1} \\ \hline \color{blue}{3x} & \color{orangered}{12x^4} & \color{orangered}{6x^2} & \color{orangered}{-3x} \\ \hline \color{blue}{-5} & \color{orangered}{-20x^3} & \color{orangered}{-10x} & \color{orangered}{5} \\ \hline \end{darray} $$Combine like terms:
$$ 12x^4 + 6x^2-20x^3-3x-10x + 5 = \\ 12x^4-20x^3+6x^2-13x+5 $$This page was created using
Polynomial Operations Calculator