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

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

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Rational Root Theorem: The Rational Root Theorem states that any rational root, in the form of p/q (where p and q are integers and q is not zero), of a polynomial equation with integer coefficients is 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 -7: ±1, ±7.Leading Coefficient Factors: List the factors of the leading coefficient 2: ±1, ±2.Generate Possible 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, ±7/1, ±1/2, ±7/2.Simplify Roots List: Simplify the list of possible rational roots: -1, 1, -7, 7, -1/2, 1/2, -7/2, 7/2.Match with Choices: Match the simplified list of possible rational roots with the given choices: (A) -1, (B) -1/2, (C) -7, (D) 7/3.Identify Possible Roots: Identify which of the possible rational roots are in the given choices: -1 (A), -1/2 (B), -7 (C). The choice (D) 7/3 is not a possible root because 3 is not a factor of the leading coefficient 2.

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