Find all of the real zeros of the polynomial function, then use the real zeros to factor f over the real numbers.

f(x) = 3x4 - 6x3 + 4x2 - 2x + 1

a. no real roots; f(x) = (x2 + 1)(3x2 + 1)

b. 1, multiplicity 2; f(x) = (x - 1)2(3x2 + 1)

c. -1, 1; f(x) = (x - 1)(x + 1)(3x2 + 1)

d. -1, multiplicity 2; f(x) = (x + 1)2(3x2 + 1)