(a) Find the rational zeros and then the other zeros of the polynomial function $f(x)=x^{3}+3 x^{2}-11 x-33$, that is, solve $f(x)=0$
(b) Factor $f(x)$ into linear factors.
(a) Select the correct choice below and fill in any answer box(es) within your choice. (Use a comma to separate answers as needed.)
A. There are only rational zeros and they are
B. There is only one rational zero, , and the other zeros are
C. There are no rational zeros. The other zeros are
(b) The factorization of $f(x)$ into linear factors is
(Type an expression using $x$ as the variable.)

Step 1 ：Use the Rational Root Theorem to find the possible rational roots of the polynomial. The possible rational roots are the factors of the constant term -33 divided by the factors of the leading coefficient 1, which are ±1, ±3, ±11, ±33.

Step 2 ：Substitute these values into the polynomial to see if they are roots. The rational root of the polynomial is -3.

Step 3 ：Use synthetic division to divide the polynomial by the factor corresponding to the rational root -3 to get a quadratic polynomial.

Step 4 ：Use the quadratic formula to find the other roots of the quadratic polynomial. The other roots are $-\sqrt{11}$ and $\sqrt{11}$, which are irrational.

Step 5 ：Factor the polynomial into linear factors using the roots. The factorization of the polynomial into linear factors is $(x + 3)(x - \sqrt{11})(x + \sqrt{11})$.

Step 6 ：\(\boxed{\text{(a) There is only one rational zero, -3, and the other zeros are } -\sqrt{11} \text{ and } \sqrt{11}.}\)

Step 7 ：\(\boxed{\text{(b) The factorization of } f(x) \text{ into linear factors is } (x + 3)(x - \sqrt{11})(x + \sqrt{11}).}\)