Answer
$c^n(3c-1)(c-3)$.
Work Step by Step
The given expression is
$=3c^{n+2}-10c^{n+1}+3c^n$
$=3c^{n}c^2-10c^{n}c+3c^n$
Factor out $c^n$.
$=c^n(3c^2-10c+3)$
Rewrite the term $-10c$ as $-9c-1c$.
$=c^n(3c^2-9c-1c+3)$
Group terms.
$=c^n[(3c^2-9c)+(-1c+3)]$
Factor from each group.
$=c^n[3c(c-3)-1(c-3)]$
Factor out $(c-3)$.
$=c^n(c-3)(3c-1)$
Rearrange.
$=c^n(3c-1)(c-3)$.
