Example 7.1.11

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*}