Question 41
Let $a, b_{1}, c_{1}, \ldots, b_{n}, c_{n}$ be real numbers such that
$$
x^{2 n}+a x^{2 n-1}+a x^{2 n-2}+\cdots+a x+1=\left(x^{2}+b_{1} x+c_{1}\right) \ldots\left(x^{2}+b_{n} x+c_{n}\right)
$$
for every real number $x$. Prove that $c_{1}=\cdots=c_{n}=1$.
$$
x^{2 n}+a x^{2 n-1}+a x^{2 n-2}+\cdots+a x+1=\left(x^{2}+b_{1} x+c_{1}\right) \ldots\left(x^{2}+b_{n} x+c_{n}\right)
$$
for every real number $x$. Prove that $c_{1}=\cdots=c_{n}=1$.