Question

A polynomial function g(x) with integer coefficients has a leading coefficient of –18 and a constant term of 3. According to the Rational Root Theorem, which of the following are possible roots of g(x)?

CHOOSE ALL THAT IS CORRECT
a) -9
b)2/3
c) 3
d) 1/6

Answer 1

The Rational Root Theorem states that any rational root of a polynomial with integer coefficients can be found by dividing the factors of the constant term by the factors of the leading coefficient. The possible roots for the given polynomial are 2/3 and 1/6.

Step-by-step explanation:

The Rational Root Theorem states that any rational root of a polynomial with integer coefficients can be found by dividing the factors of the constant term by the factors of the leading coefficient. In this case, the leading coefficient is -18 and the constant term is 3. To find the possible roots, we need to find the factors of -18 and 3. The factors of -18 are -1, 1, -2, 2, -3, 3, -6, and 6. The factors of 3 are -1, 1, -3, and 3. By dividing these factors, we get the possible rational roots -1/3, 1/3, -2/3, 2/3, -1, 1, -3, 3, -1/2, 1/2, -3/2, and 3/2. So, the correct answers are b) 2/3 and d) 1/6.