Answer :
Final answer:
The polynomial function with the given zeros (-4, -1, 0, 1, 4) is
Option 1: f(x) =[tex]5x^5 - 173x^3 + 16[/tex].
The polynomial was derived using the fact that when 'a' is a zero, (x-a) is a factor, and vice versa.
Explanation:
The question seeks to identify a polynomial function with given zeros.
Keep in mind, if 'a' is a zero of the polynomial function f(x) then (x-a) is a factor of the polynomial.
Conversely, if (x-a) is a factor of the polynomial, 'a' is a zero of the function.
The zeros provided are -4, -1, 0, 1, and 4.
So, the polynomial function can be written in the form f(x) = [tex]k(x+4)(x+1)(x)(x-1)(x-4)[/tex] where k is a constant.
Among the options given, the function that is built using our model is
Option 1: f(x) = [tex]5x^5 - 173x^3 + 16[/tex].
Learn more about Polynomial Functions here:
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