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Answer :
Final answer:
By applying the Factor Theorem and multiplying the corresponding factors of the given zeros, it is found that the polynomial function d) f(x) = x^3 - 4x^2 - 7x + 28 is the correct answer.
Explanation:
In this exercise, we are applying the Factor Theorem to identify which polynomial function has the zeros 4, √7, and -√7. By the Factor Theorem, if a polynomial f(x) has a zero (or root) c, then (x-c) is a factor of the polynomial. Given the zeros 4, √7, and -√7, the corresponding factors would be (x-4), (x-√7), and (x+√7).
Multiplying these factors together, you will get the polynomial function x^3 - 4x^2 - 7x + 28. Therefore, the correct polynomial function that has the zeros 4, √7, and -√7 is f(x) = x^3 - 4x^2 - 7x + 28.
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