High School

According to the Rational Root Theorem, which function has the same set of potential rational roots as the function \( g(x) = 35x^4 - 29x^3 - 22x + 122 \)?

A. \( f(x) = 3x^5 - 24x - 93x^2 - 12 \)

B. \( f(x) = 35x^4 - 25x + 94x^3 - 13 + 12x \)

C. \( f(x) = 125x^4 - 24x^3 - 2x - 3 \)

D. \( f(x) = 125x^4 - 84x + 35x^3 - 42x^2 - 43 \)

Answer :

Final answer:

The function D) = 125-844 +353-42.43 has the same set of potential rational roots as g(x) = 35-293-22.122.

Explanation:

The function g(x) = 35-293-22.122 has the same set of potential rational roots as the function D) = 125-844 +353-42.43. According to the Rational Root Theorem, the potential rational roots of a polynomial function can be found by considering the factors of the constant term and the leading coefficient.

In this case, the constant term of function D) is 125 and its leading coefficient is 1. The factors of 125 are ±1, ±5, ±25, ±125, and the factors of 1 are ±1. Therefore, the potential rational roots are ±1, ±5, ±25, and ±125.

Since the potential rational roots of function D) match the potential rational roots of g(x), D) is the function that has the same set of potential rational roots.

Learn more about Rational Root Theorem here:

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