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

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A polynomial function g(x) with integer coefficients has a leading coefficient of -7 and a constant term of -3. According to the Rational Root Theorem, which of the following are possible roots of g(x)?   Multi-select Choices: (A)-1 (B)-1/7 (C)1/7 (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.Factor Constant Term: List the factors of the constant term -3: ±1, ±3.Factor Leading Coefficient: List the factors of the leading coefficient -7: ±1, ±7.Generate Possible Rational Roots: Generate the possible rational roots by taking all combinations of the factors of the constant term over the factors of the leading coefficient: ±1/1, ±1/7, ±3/1, ±3/7.Simplify Roots List: Simplify the list of possible rational roots: -1, 1, -1/7, 1/7, -3, 3, -3/7, 3/7.Match with Given Choices: Match the simplified list of possible rational roots with the given choices: (A) -1, (B) -1/7, (C) 1/7, (D) 1.Identify Correct Choices: Identify the correct choices from the list that are also given in the multi-select options: (A) -1, (B) -1/7, (C) 1/7, (D) 1.

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