A polynomial function h(x) with integer coefficients has a leading coefficient of 8 and a constant term of 2. According to the Rational Root Theorem, which of the following are possible roots of h(x)? Multi-select Choices: (A)1/8 (B)2 (C)1/4 (D)-18/17

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A polynomial function h(x) with integer coefficients has a leading coefficient of 8 and a constant term of 2. According to the Rational Root Theorem, which of the following are possible roots of h(x)?   Multi-select Choices: (A)1/8 (B)2 (C)1/4 (D)-18/17

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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 with no common factors other than 1 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.Identify Constant Term Factors: Identify the factors of the constant term, which is 2. The factors of 2 are ±1 and ±2.Identify Leading Coefficient Factors: Identify the factors of the leading coefficient, which is 8. The factors of 8 are ±1, ±2, ±4, and ±8.List Possible Rational Roots: List all possible rational roots by combining the factors of the constant term with the factors of the leading coefficient. The possible rational roots are ±1/8, ±1/4, ±1/2, ±1, ±2/8, ±2/4, ±2/2, and ±2.Simplify Rational Roots List: Simplify the list of possible rational roots to remove duplicates and improper fractions: ±1/8, ±1/4, ±1/2, ±1, ±2.Compare with Given Choices: Compare the simplified list of possible rational roots with the given choices. The possible roots from the choices are: (A) 1/8 (since 1 is a factor of 2 and 8 is a factor of 8) (B) 2 (since 2 is a factor of 2 and 1 is a factor of 8) (C) 1/4 (since 1 is a factor of 2 and 4 is a factor of 8) (D) -18/17 is not a possible root because neither 18 is a factor of 2 nor 17 is a factor of 8.

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