Question: Consider the following polynomial. \[ m(x) = 3x^4 - 13x^3 + x^2 + 13x - 4 \] Step 1 of 2: Use…

Consider the following polynomial.

\[ m(x) = 3x^4 - 13x^3 + x^2 + 13x - 4 \]

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

Step 1: Identify the factors of the constant term and the leading coefficient. \[ \text{Constant term (p)} = -4 \\ \text{Factors of } p: \pm1, \pm2, \pm4 \] \[ \text{Leading coefficient (q)} = 3 \\ \text{Factors of } q: \pm1, \pm3 \] Step 2: Use the Rational Zero Theorem to list all possible rational zeros. \[ \frac{p}{q} = \pm1, \pm\frac{1}{3}, \pm2, \pm\frac{2}{3}, \pm4, \pm\frac{4}{3} \] Since only positive values are required, the potential rational zeros are: 1, 1/3, 2, 2/3, 4, 4/3