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:

The polynomial function with the zeros 4, √7, and -√7 is represented by option B) f(x) = x³ - 4x² + 7x - 28.

Explanation:

To find the polynomial function with the given zeros, we will use the factor theorem. The factor theorem states that if a is a zero of a polynomial function, then (x - a) is a factor of the polynomial.

Using this theorem, we can determine that the polynomial function with zeros 4, √7, and -√7 is represented by option B) f(x) = x³ - 4x² + 7x - 28.

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