Let F be a field and let a be a nonzero element of F. (a) If af(x) is irreducible over F, prove that f(x) is irreducible over F. (b) If f(x + a) is irreducible over F, prove that f(x) is irreducible...

Extracted text: Let F be a field and let a be a nonzero element of F. (a) If af(x) is irreducible over F, prove that f(x) is irreducible over F. (b) If f(x + a) is irreducible over F, prove that f(x) is irreducible of over F. (c) Use part b) to prove that f(x) = 8r³ – 6x+1 is irreducible over Q. Hint: Consider f(x + 1).