For f(x) = 3x cubed + 2x squared - 7x + 4, which value is NOT a possible rational zero?

1. The Rational Zero Theorem builds candidates as a factor of the constant over a factor of the leading coefficient. 2. The constant term is 4, so the numerators are 1, 2 and 4, positive or negative. 3. The leading coefficient is 3, so the denominators are 1 and 3, positive or negative. 4. That gives candidates of 1, 2, 4, one third, two thirds and four thirds, with both signs. 5. The value 1 over 2 needs a denominator of 2, but 2 is not a factor of the leading coefficient 3. 6. So 1 over 2 cannot be a rational zero of this polynomial. 7. The values 4 over 3 and 2 over 3 both fit, since 4 and 2 divide the constant and 3 divides the leading coefficient. 8. The value 4 over 1 fits, since 4 divides the constant and 1 divides the leading coefficient. _Source: OpenStax Precalculus (CC BY 4.0), section 3.6 Zeros of Polynomial Functions_