A polynomial function g(x) with integer coefficients has a leading coefficient of -2 and a constant term of 8. According to the Rational Root Theorem, which of the following are possible roots of g(x)? Multi-select Choices: (A)-12/7 (B)11/20 (C)-5/3 (D)1

Question

A polynomial function g(x) with integer coefficients has a leading coefficient of -2 and a constant term of 8. According to the Rational Root Theorem, which of the following are possible roots of g(x)?   Multi-select Choices: (A)-12/7 (B)11/20 (C)-5/3 (D)1

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Understand Rational Root Theorem: The Rational Root Theorem states that any rational root, in the form of p/q (where p and q are integers), of the polynomial equation with integer coefficients must have p as a factor of the constant term and q as a factor of the leading coefficient.Factors of Constant Term: List the factors of the constant term 8: ±1, ±2, ±4, ±8.Factors of Leading Coefficient: List the factors of the leading coefficient -2: ±1, ±2.Generate Possible Rational Roots: Generate all possible rational roots by combining the factors of the constant term with the factors of the leading coefficient: ±1/1, ±2/1, ±4/1, ±8/1, ±1/2, ±2/2, ±4/2, ±8/2.Simplify List of Roots: Simplify the list of possible rational roots: ±1, ±2, ±4, ±8, ±1/2, ±4/2.Check Options Against List: Further simplify the list by removing duplicates and unnecessary fractions: ±1, ±2, ±4, ±8, ±1/2.Check each option against the list of possible rational roots: (A) -12/7 is not in the list, so it's not a possible root. (B) 11/20 is not in the list, so it's not a possible root. (C) -5/3 is not in the list, so it's not a possible root. (D) 1 is in the list, so it is a possible root.

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