Question 3
Let $f(x)=a_nx^n+a_{n-1}x^{n-1}+\cdots+a_0$ and $g(x)=c_{n+1}x^{n+1}+c_nx^n+\cdots+c_0$ be nonzero polynomials with real coefficients such that $g(x)=(x+r)f(x)$ for some real $r$. If $a=\max(|a_n|,\ldots,|a_0|)$ and $c=\max(|c_{n+1}|,\ldots,|c_0|)$, prove that $a/c\le n+1$.