1. List all possible rational zeros of f(x)=3x^4-11x^3-x^2+19x+6

To find the possible rational zeros of the polynomial function \( f(x) = 3x^4 - 11x^3 - x^2 + 19x + 6 \), we can use the Rational Root Theorem. This theorem states that any rational zero, expressed as , must have as a factor of the constant term and as a factor of the leading coefficient.For the polynomial \( f(x) = 3x^4 - 11x^3 - x19x + 6 \):1. The constant term is .2. The leading coefficient is .First, list the factors of the constant term : Next, list the factors of the leading coefficient : Now, form all possible fractions where is a factor of the constant term and is a factor of the leading coefficient: So, the list of all possible rational zeros is: Therefore, the possible rational zeros of the polynomial \( f(x) = 3x^4 - 11x^3 - x^2 + 19x + 6 \) are: