Final answer:
The factor of the quadratic function corresponding to the zero at 2/3 is 3x - 2; therefore, the correct answer is d. 3x - 2.
Step-by-step explanation:
The student has asked for help with determining one factor of a quadratic function that has zeros at -4/3 and 2/3. A zero of a quadratic function corresponds to the x-value where the function equals zero, and can be represented by the factor (x - zero). Therefore, if the function has a zero at -4/3, one factor must be (x - (-4/3)) or (x + 4/3), and if the other zero is at 2/3, the factor must be (x - 2/3).
When we clear the fractions in these expressions, we multiply the inside of the parentheses by 3 to get rid of the denominator, resulting in factors of 3x + 4 and 3x - 2. The correct factor that corresponds to one of these zeros and is available in the options provided by the student is 3x - 2, which corresponds to the zero at 2/3.
The answer to the question is d. 3x - 2.