A polynomial function f(x) with integer coefficients has a leading coefficient of 1 and a constant term of -14. According to the Rational Root Theorem, which of the following are possible roots of f(x)? Multi-select Choices: (A)-7 (B)7/2 (C)14 (D)-14

Question

A polynomial function f(x) with integer coefficients has a leading coefficient of 1 and a constant term of -14. According to the Rational Root Theorem, which of the following are possible roots of f(x)?   Multi-select Choices: (A)-7 (B)7/2 (C)14 (D)-14

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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.Leading Coefficient: Since the leading coefficient is 1, any rational root will have a denominator of 1, meaning it must be an integer.Factors of Constant Term: List the factors of the constant term -14: ±1, ±2, ±7, ±14.Checking Potential Roots: Check each option against the list of factors: (A) -7 is a factor of -14, so it could be a root. (B) 7/2 is not an integer, so it cannot be a root. (C) 14 is a factor of -14, so it could be a root. (D) -14 is a factor of -14, so it could be a root.

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