A polynomial function f(x) with integer coefficients has a leading coefficient of -5 and a constant term of 2. According to the Rational Root Theorem, which of the following are possible roots of f(x)? Multi-select Choices: (A)-1/5 (B)2/17 (C)2 (D)10/3

Question

A polynomial function f(x) with integer coefficients has a leading coefficient of -5 and a constant term of 2. According to the Rational Root Theorem, which of the following are possible roots of f(x)?   Multi-select Choices: (A)-1/5 (B)2/17 (C)2 (D)10/3

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Understand Rational Root Theorem: The Rational Root Theorem states that any rational root, expressed in its simplest form p/q, must have p as a factor of the constant term and q as a factor of the leading coefficient.Factor Constant Term: List the factors of the constant term 2: ±1, ±2.Factor Leading Coefficient: List the factors of the leading coefficient -5: ±1, ±5.Generate Possible Rational Roots: Generate the possible rational roots by combining the factors of the constant term with the factors of the leading coefficient: ±1/1, ±1/5, ±2/1, ±2/5.Simplify Roots List: Simplify the list of possible rational roots: -1, -1/5, 1, 1/5, -2, -2/5, 2, 2/5.Check Given Options: Check the given options against the list of possible rational roots. (A) -1/5 is in the list, so it's a possible root. (B) 2/17 is not in the list because 17 is not a factor of the leading coefficient -5. (C) 2 is in the list, so it's a possible root. (D) 10/3 is not in the list because 3 is not a factor of the leading coefficient -5.

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