Final answer:
To find a polynomial with zeros at -4 and 6, we create factors (x + 4) and (x - 6), hence the correct polynomial function is f(x) = (x + 4)(x - 6).
Step-by-step explanation:
The student is asking to find a polynomial function with zeros at -4 and 6. To find a polynomial with zeros at -4 and 6, we create factors (x + 4) and (x - 6), hence the correct polynomial function is f(x) = (x + 4)(x - 6).
To find a polynomial with given zeros, we use the fact that if x=a is a zero of the polynomial, then (x-a) is a factor of that polynomial. In this case, the factors would be (x - (-4)) or (x + 4), and (x - 6).
Thus, the polynomial with zeros at -4 and 6 will be f(x) = (x + 4)(x - 6). This multiplies out to x² - 2x - 24 but the multiplication is not necessary for answering this question.
Therefore, the correct answer is:
a) f(x) = (x + 4)(x - 6)