The kernel of an evaluation morphism

Let Z[X] be the ring of polynomials with integer coefficients, and let KZ[X] be the kernel of the "evaluation at 1" homomorphism

ε1:Z[X]Z3f(X)[f(1)]3.
  1. Characterize K as a set.
  2. Determine whether K is a maximal ideal. Fully justify your conclusion.
  3. Determine whether K is a principal ideal. Justify by either exhibiting a generator or proving that there isn't one.