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.

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the first one

step-by-step explanation:

just id the test.