So I'm looking at Rudin's principles of mathematical analysis theorem 8.8 (fundamental theorem of algebra):
Suppose $c_1, ..., c_n$ are complex numbers, $n\geq1,\;a_n\neq0$, $$P(z) = \sum_0^na_kz^k.$$ Then $P(z) = 0$ for some complex $z$.
The proof starts with the sentence:
Without loss of generality, assume $a_n =1$.
And I'm not entirely sure why this is even allowed. It would be great if someone could explain this to me?