# Math Help - monic polynomials

1. ## monic polynomials

Any ideas on this one?

Let f(x) be a monic polynomial over Z. Show that if n is a nonzero integer such that f(n) = 0, then n divides f(0).

Thanks!

2. $f(x)=x^k + a_{k-1}x^{k-1} + ... + a_1x + a_0$
$f(n)=n^k + a_{k-1}n^{k-1} + ... + a_1n + a_0=0$
$n^k + a_{k-1}n^{k-1} + ... + a_1n =- a_0$
n divides the left side, so n divides $a_0=f(0)$

3. Originally Posted by hka210
Any ideas on this one?

Let f(x) be a monic polynomial over Z. Show that if n is a nonzero integer such that f(n) = 0, then n divides f(0).

Thanks!
If f(n)= 0, then (x- n) is a factor of f(x).