Part 1 of 3

Use the following function to answer parts a through c.
\[
f(x)=11 x^{3}+124 x^{2}+34 x+11
\]
a. List all possible rational zeros.
(Type an integer or a simplified fraction. Use a comma to separate answers

Step 1 ：Given the function \(f(x)=11 x^{3}+124 x^{2}+34 x+11\)

Step 2 ：The Rational Root Theorem states that any rational root, \(p/q\), of a polynomial equation, where \(p\) and \(q\) are integers, \(p\) is a factor of the constant term, and \(q\) is a factor of the leading coefficient.

Step 3 ：In this case, the constant term is 11 and the leading coefficient is 11. So, we need to find all the factors of 11 and 11, and then form all possible combinations of these factors, considering both positive and negative values.

Step 4 ：The factors of the constant term 11 are \(1, 11\)

Step 5 ：The factors of the leading coefficient 11 are \(1, 11\)

Step 6 ：Forming all possible combinations of these factors, considering both positive and negative values, we get the possible rational zeros as \(\frac{1}{11}, 1, -\frac{1}{11}, 11, -11, -1\)

Step 7 ：Final Answer: The possible rational zeros of the function are \(\boxed{\frac{1}{11}, 1, -\frac{1}{11}, 11, -11, -1}\)