Final answer:
Using the Rational Root Theorem, the possible rational zeros of the function f(x) = 3x^5 + 7x^3 - 3x^2 + 2 are ±1, ±2, ±1/3, ±2/3.
Step-by-step explanation:
To find the possible rational zeros of the polynomial function f(x) = 3x5 + 7x3 - 3x2 + 2, we can use the Rational Root Theorem. This theorem states that any rational zero, which is expressed in the form of p/q (where p is a factor of the constant term and q is a factor of the leading coefficient), must come from a list of possible fractions generated by taking all the factors of the constant term and dividing them by all the factors of the leading coefficient.
The constant term 2 has factors of ±1 and ±2. The leading coefficient 3 has factors of ±1 and ±3. We can create a list of all possible rational zeros by dividing each factor of the constant term (the numerator) by each factor of the leading coefficient (the denominator).
So the possible rational zeros of the function can be listed as answer choice (b): ±1, ±2, ±1/3, ±2/3.