Thread: 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!

n divides the left side, so n divides

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).