Question
Multiply polynomial $ \, \color{blue}{ 4x^2+8x-41 } \, $ by $ \, \color{orangered}{ x-4 }$.
Answer
$$ \left( \color{blue}{4x^2+8x-41} \right) \cdot \left( \color{orangered}{x-4} \right) = 4x^3-8x^2-73x+164 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{4x^2} & \color{blue}{8x} & \color{blue}{-41} \\ \hline \color{blue}{x} & & & \\ \hline \color{blue}{-4} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{4x^2} & \color{blue}{8x} & \color{blue}{-41} \\ \hline \color{blue}{x} & \color{orangered}{4x^3} & \color{orangered}{8x^2} & \color{orangered}{-41x} \\ \hline \color{blue}{-4} & \color{orangered}{-16x^2} & \color{orangered}{-32x} & \color{orangered}{164} \\ \hline \end{darray} $$Combine like terms:
$$ 4x^3 + 8x^2-16x^2-41x-32x + 164 = \\ 4x^3-8x^2-73x+164 $$This page was created using
Polynomial Operations Calculator