Re: a question about reducible polynomials


amanda wrote:
if f(x) is a polynomial of integral coefficients with deg(f)=n, then why there are infinitely many integers m such that f(x)-m is reducible over Q[x], where Q means rationals.
thanks

This sounds like homework, so let me offer a way for you to think it
through for yourself.

What value(s) of m would allow f(x) - m to have a factor of low degree?
As Peter points out the polynomial f(x) cannot be reducible if deg(f)
= 1, but what condition on m would give a factor of f(x) - m of degree
1?

regards, chip

.

Loading