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)-3 (D)1/2

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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)-3 (D)1/2

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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.Constant Term Factors: List the factors of the constant term -3: ±1, ±3.Leading Coefficient Factors: List the factors of the leading coefficient -7: ±1, ±7.Generate Possible Roots: Generate the possible rational roots by combining the factors of the constant term with the factors of the leading coefficient: ±1/1, ±1/7, ±3/1, ±3/7.Simplify Roots: Simplify the possible rational roots: ±1, ±1/7, ±3, ±3/7.Match with Choices: Match the simplified possible roots with the given choices: (A) 1, (B) 1/7, (C) -3, (D) 1/2.Choice (A): Choice (A) 1 is a possible root because 1 is a factor of -3.Choice (B): Choice (B) 1/7 is a possible root because 1 is a factor of -3 and 7 is a factor of -7.Choice (C): Choice (C) -3 is a possible root because -3 is a factor of -3.Choice (D): Choice (D) 1/2 is not a possible root because 2 is not a factor of -7.

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