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

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A polynomial function g(x) with integer coefficients has a leading coefficient of -5 and a constant term of -2. According to the Rational Root Theorem, which of the following are possible roots of g(x)?   Multi-select Choices: (A)-1 (B)-2 (C)-1/5 (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 a polynomial equation with integer coefficients must be such that p is a factor of the constant term and q is a factor of the leading coefficient.Factors of Constant Term: List the factors of the constant term -2: ±1, ±2.Factors of Leading Coefficient: List the factors of the leading coefficient -5: ±1, ±5.Generate Possible Rational Roots: Generate the possible rational roots by combining the factors of the constant term with the factors of the leading coefficient: ±1/1, ±2/1, ±1/5, ±2/5.Simplify Roots: Simplify the possible rational roots: -1, 1, -2, 2, -1/5, 1/5, -2/5, 2/5.Match with Given Choices: Match the simplified possible roots with the given choices: (A) -1, (B) -2, (C) -1/5, (D) 1.

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