High School

Using the Factor Theorem, which of the polynomial functions has the zeros 4, [tex]\sqrt{7}[/tex], and [tex]-\sqrt{7}[/tex]?

A) [tex]f(x) = x^3 - 4x^2 - 7x + 28[/tex]

B) [tex]f(x) = x^3 - 4x^2 + 7x - 28[/tex]

C) [tex]f(x) = x^3 + 4x^2 - 7x + 28[/tex]

D) [tex]f(x) = x^3 + 4x^2 + 7x - 28[/tex]

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.

Learn more about Factor Theorem here:

https://brainly.com/question/35460223

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