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Using the rational root theorem, list out all possible/candidate rational roots of $f(x)=2 x^{3}-28 x^{2}-5$. Express your answer as integers or as fractions in simplest form. Use commas to separate.
Answer Attempt 1 out of 2

Step 1 ：The Rational Root Theorem states that if a polynomial has a rational root, then it must be a factor of the constant term divided by a factor of the leading coefficient.

Step 2 ：In this case, the constant term is -5 and the leading coefficient is 2.

Step 3 ：So, we need to list out all the factors of -5 and 2, and form all possible fractions by dividing a factor of -5 by a factor of 2.

Step 4 ：We also need to consider both positive and negative values, because a positive divided by a negative is a negative, and a negative divided by a positive is also a negative.

Step 5 ：The factors of the constant term -5 are 1 and 5.

Step 6 ：The factors of the leading coefficient 2 are 1 and 2.

Step 7 ：By forming all possible fractions by dividing a factor of -5 by a factor of 2, we get the possible roots as 1, 5, \(\frac{1}{2}\), -\(\frac{1}{2}\), -5, \(\frac{5}{2}\), -1, -\(\frac{5}{2}\).

Step 8 ：Final Answer: The possible rational roots of the polynomial \(f(x)=2 x^{3}-28 x^{2}-5\) are \(\boxed{1, 5, \frac{1}{2}, -\frac{1}{2}, -5, \frac{5}{2}, -1, -\frac{5}{2}}\).