A polynomial function f(x) with integer coefficients has a leading coefficient of 1 and a constant term of -16. According to the Rational Root Theorem, which of the following are possible roots of f(x)? Multi-select Choices: (A)-1 (B)-14 (C)-4/5 (D)-3

Question

A polynomial function f(x) with integer coefficients has a leading coefficient of 1 and a constant term of -16. According to the Rational Root Theorem, which of the following are possible roots of f(x)?   Multi-select Choices: (A)-1 (B)-14 (C)-4/5 (D)-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 must be a factor of the constant term divided by a factor of the leading coefficient.Factors of Constant Term: Since the leading coefficient is 1, any rational root must be a factor of the constant term -16. The factors of -16 are ±1, ±2, ±4, ±8, and ±16.Checking Options: Check each of the given options against the factors of -16. (A) -1 is a factor of -16, so it could be a root. (B) -14 is not a factor of -16, so it cannot be a root. (C) -4/5 is not an integer and thus cannot be a root since the coefficients are integers. (D) -3 is not a factor of -16, so it cannot be a root.

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