A polynomial function f(x) with integer coefficients has a leading coefficient of 3 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)1 (B)-1/3 (C)1/3 (D)-19

Question

A polynomial function f(x) with integer coefficients has a leading coefficient of 3 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)1 (B)-1/3 (C)1/3 (D)-19

Bytelearn · Accepted Answer

List Factors Constant Term: List all possible factors of the constant term, which is 1. The factors of 1 are ±1.List Factors Leading Coefficient: List all possible factors of the leading coefficient, which is 3. The factors of 3 are ±1 and ±3.Possible Rational Roots: According to the Rational Root Theorem, the possible rational roots are the factors of the constant term divided by the factors of the leading coefficient. So, we get ±1/1, ±1/3.Simplify Roots: Simplify the possible rational roots. We have 1, -1, 1/3, and -1/3.Check Given Choices: Check the given choices against the possible roots we found. Choices (A) 1, (B) -1/3, and (C) 1/3 are the possible roots. Choice (D) -19 is not a possible root because 19 is not a factor of the constant term 1.

Full solution

More problems from Rational root theorem

Related topics