Example7.1.11

Factor $$14-7n^2+28n^4-21n\text{.}$$

Notice that the terms are not in a standard order, with powers of $$n$$ decreasing as you read left to right. It is usually a best practice to rearrange the terms into the standard order first.

\begin{equation*} 14-7n^2+28n^4-21n=28n^4-7n^2-21n+14\text{.} \end{equation*}

The number $$7$$ divides all of the numerical coefficients. Separately, no power of $$n$$ is part of the greatest common factor because the $$14$$ term has no $$n$$ factors. So the greatest common factor is just $$7\text{.}$$ We proceed by factoring that out:

\begin{align*} 14-7n^2+28n^4-21n\amp=28n^4-7n^2-21n+14\\ \amp=7\mathopen{}\left(4n^4-n^2-3n+2\right)\mathclose{} \end{align*}
in-context