A polynomial function f(x) with integer coefficients has a leading coefficient of 2 and a constant term of 1. According to the Rational Root Theorem, which of the following are possible roots of f(x)? Multi-select Choices: (A)4/3 (B)1/2 (C)1 (D)1/10

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A polynomial function f(x) with integer coefficients has a leading coefficient of 2 and a constant term of 1. According to the Rational Root Theorem, which of the following are possible roots of f(x)?   Multi-select Choices: (A)4/3 (B)1/2 (C)1 (D)1/10

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Understand Rational Root Theorem: The Rational Root Theorem states that any rational root, expressed in its lowest terms p/q, must have p as a factor of the constant term and q as a factor of the leading coefficient.List Factors of Constant Term: List the factors of the constant term, which is 1: ±1.List Factors of Leading Coefficient: List the factors of the leading coefficient, which is 2: ±1, ±2.Form Possible Fractions: Form all possible fractions p/q using the factors of the constant term for p and the factors of the leading coefficient for q: ±1/1, ±1/2.Simplify Fractions: Simplify the fractions to get the possible rational roots: ±1, ±1/2.Check Given Options: Check the given options against the possible rational roots: (A) 4/3 is not a possible root because 3 is not a factor of the leading coefficient. (B) 1/2 is a possible root. (C) 1 is a possible root. (D) 1/10 is not a possible root because 10 is not a factor of the leading coefficient.

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