A polynomial function g(x) with integer coefficients has a leading coefficient of -1 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 (C)-7 (D)-3

Question

A polynomial function g(x) with integer coefficients has a leading coefficient of -1 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 (C)-7 (D)-3

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Rational Root Theorem: The Rational Root Theorem states that any rational root, in the form of p/q (where p is a factor of the constant term and q is a factor of the leading coefficient), must be an integer since the leading coefficient is -1.List Factors of Constant Term: List the factors of the constant term, which is 3. The factors are ±1 and ±3.Identify Possible Rational Roots: Since the leading coefficient is -1, the possible rational roots are the factors of the constant term, which are ±1 and ±3.Check Choices Against Possible Roots: Check the choices given against the possible roots. The possible roots are -1, 1, -3, and 3.Match Possible Roots to Choices: Match the possible roots to the choices given: (A) -1, (B) 1, and (D) -3 are the correct matches. Choice (C) -7 is not a factor of the constant term, so it cannot be a root.

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