### (a) If R is a unique factorization domain, prove that every f(x) belongs to R[x] can be written as f(x) = af_1(x) where a belongs to R and where f_1(x) is primitive, (b) Prove that the decomposition in part (a) is unique ( up to associate).

Modern Algebra Ring Theory (XLVIII) Unique Factorization Domain Greatest Common Divisor Relatively Prime Elements