Question: Consider the following polynomial. \[ g(x) = 4x^4 + 28x^3 + 47x^2 - 7x - 12 \] Step 1 of 2: Use…

Consider the following polynomial.

\[ g(x) = 4x^4 + 28x^3 + 47x^2 - 7x - 12 \]

Step 1 of 2: Use the Rational Zero Theorem to list all of the potential rational zeros.

Answer

Enter only the positive values. Separate multiple answers with commas.

\[ \pm \{ \} \]

Solution

Identify the factors of the constant term and the leading coefficient. \[ \text{Factors of } -12: 1, 2, 3, 4, 6, 12 & \] \[ \text{Factors of } 4: 1, 2, 4 & \] List all possible positive rational zeros \( \frac{p}{q} \). \[ 1, \frac{1}{2}, \frac{3}{2}, \frac{3}{4}, 2, 3, 6, 12 & \]