Question

use the following function to answer parts a through c. f(x)=5x^{3}+27x^{2}+11x + 5

a. list all possible rational zeros.

(type an integer or a simplified fraction. use a comma to separate answers as needed. type each answer only once.)

Explanation:

Step1: Identify leading - coefficient and constant

For the polynomial $f(x)=5x^{3}+27x^{2}+11x + 5$, the leading - coefficient $a_{n}=5$ and the constant term $a_{0}=5$.

Step2: Find factors of leading - coefficient and constant

The factors of the leading - coefficient $a_{n}=5$ are $\pm1,\pm5$. The factors of the constant term $a_{0}=5$ are $\pm1,\pm5$.

Step3: Apply the Rational Zero Theorem

The possible rational zeros are of the form $\frac{p}{q}$, where $p$ is a factor of the constant term and $q$ is a factor of the leading - coefficient. So, $\frac{p}{q}=\pm1,\pm5,\pm\frac{1}{5}$.

Answer:

$1, - 1,5,-5,\frac{1}{5},-\frac{1}{5}$