Which statement about the polynomial function g(x) is true?
if all rational roots of g(x) = 0 are integers, the leading coefficient of g(x) must be 1.
if all roots of g(x) = 0 are integers, the leading coefficient of g(x) must be 1.
if the leading coefficient of g(x) is 1, all rational roots of g(x) = 0 must be integers.
if the leading coefficient of g(x) is 1, all roots of g(x) = 0 must be integers.

The correct answer is:

If the leading coefficient of g(x) is 1, all rational roots of g(x) = 0 must be integers.

Explanation:

The Rational Root Theorem states:

If P(x) is a polynomial with integer coefficients and if p/q is a zero of P(x) (P(p/q)=0), then p is a factor of the constant term of P(x) and q is a factor of the leading coefficient of P(x).

If p(x) is an nth degree monic polynomial (has a leading coefficient of 1) with integer coefficients, then a consequence of the Rational Root Theorem is:

If p(x) has at least one rational root, then each of its rational roots or zeros, must be an integer.

where did you get them? if you picked from the grass, is is probably poisonous.

step-by-step explanation: