According to the Rational Root Theorem, -7/8 is a potential rational root of which function?
A) f(x) = 24x⁷ + 3x⁶ + 4x³ - x - 28
B) f(x) = 28x⁷ + 3x⁶ + 4x³ - x - 24
C) f(x) = 30x⁷ + 3x⁶ + 4x³ - x - 56
D) f(x) = 56x⁷ + 3x⁶ + 4x³ - x - 30

Solution:

We have to find -7/8  is a potential rational root of which of the given functions.

From the options,

a) f(x) = 24x⁷ + 3x⁶ + 4x³ - x - 28

Factors of constant term 28 are 1, 2, 4, 7, 14, 28

Factors of leading coefficient 24 are 1, 2, 3, 4, 6, 8, 12, 24

Ratios are (± 1, 2, 4, 7, 14, 28)/(± 1, 2, 3, 4, 6, 8, 12, 24)

-7/8 is a potential root of the function f(x).

b) f(x) = 28x⁷ + 3x⁶ + 4x³ - x - 24

Factors of constant term 24 are 1, 2, 3, 4, 6, 8, 12, 24 

Factors of leading coefficient 28 are 1, 2, 4, 7, 14, 28

Ratios are (± 1, 2, 3, 4, 6, 8, 12, 24)/ (± 1, 2, 4, 7, 14, 28)

-7/8 is not a potential root of the function f(x).

c) f(x) = 30x⁷ + 3x⁶ + 4x³ - x - 56

Factors of constant term 56 are 1, 2, 4, 7, 8, 14, 28, 56

Factors of leading coefficient 30 are 1, 2, 3, 5, 6, 10,15, 30

Ratios are (± 1, 2, 4, 7, 8, 14, 28, 56)/(± 1, 2, 3, 5, 6, 10,15, 30)

-7/8 is not a potential root of the function f(x).

d) f(x) = 56x⁷ + 3x⁶ + 4x³ - x - 30

Factors of constant term 56 are 1, 2, 3, 5, 6, 10,15, 30

Factors of leading coefficient 30 are 1, 2, 4, 7, 8, 14, 28, 56

Ratios are (± 1, 2, 3, 5, 6, 10,15, 30 )/(± 1, 2, 4, 7, 8, 14, 28, 56)

-7/8 is not a potential root of the function f(x).

Therefore, -7/8 is a potential root of the function f(x) = 24x⁷ + 3x⁶ + 4x³ - x - 28.

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According to the Rational Root Theorem, -7/8 is a potential rational root of which function?

Summary:

-7/8 is a potential root of the function f(x) = 24x⁷ + 3x⁶ + 4x³ - x - 28.