Exercise
Let f be an irreducible polynomial which divides the product of polynomials f1f2 ··· fn. Then
f divides some of the fi.
there is an index i with f = fi.
all the fi have a smaller degree than f.
Yes. (Can you prove it?)
No, this is not correct. Look for example at the case where n = 1.
No, read the section on factorization of polynomials again.