Question
Multiply polynomial $ \, \color{blue}{ x^4-8x+16 } \, $ by $ \, \color{orangered}{ x-4 }$.
Answer
$$ \left( \color{blue}{x^4-8x+16} \right) \cdot \left( \color{orangered}{x-4} \right) = x^5-4x^4-8x^2+48x-64 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^4} & \color{blue}{-8x} & \color{blue}{16} \\ \hline \color{blue}{x} & & & \\ \hline \color{blue}{-4} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^4} & \color{blue}{-8x} & \color{blue}{16} \\ \hline \color{blue}{x} & \color{orangered}{x^5} & \color{orangered}{-8x^2} & \color{orangered}{16x} \\ \hline \color{blue}{-4} & \color{orangered}{-4x^4} & \color{orangered}{32x} & \color{orangered}{-64} \\ \hline \end{darray} $$Combine like terms:
$$ x^5-8x^2-4x^4 + 16x + 32x-64 = \\ x^5-4x^4-8x^2+48x-64 $$This page was created using
Polynomial Operations Calculator